LIFE LEXICON Release 25, 2006 February 28 ASCII version INTRODUCTION This is a lexicon of terms relating to John Horton Conway's Game of Life. It is also available in single-page and multipage HTML versions. This lexicon was compiled by Stephen A. Silver - see below for additional credits. I can be contacted at life(at)argentum.freeserve.co.uk. The latest versions of this lexicon (both HTML and ASCII) should be available from the Life Lexicon Home Page at http://www.argentum.freeserve.co.uk/lex_home.htm. CREDITS The largest single source for the early versions of this lexicon was a glossary compiled by Alan Hensel "with indispensable help from John Conway, Dean Hickerson, David Bell, Bill Gosper, Bob Wainwright, Noam Elkies, Nathan Thompson, Harold McIntosh, and Dan Hoey". Other sources include the works listed in the bibliography at the end of this lexicon, as well as pattern collections by Alan Hensel and David Bell (and especially Dean Hickerson's file stamp.l in the latter collection), and the web sites of Mark Niemiec, Paul Callahan, Achim Flammenkamp, Robert Wainwright and Heinrich Koenig. Recent releases also use a lot of information from Dean Hickerson's header to his 1995 stamp file (http://math.ucdavis.edu/~dean/RLE/stamps.html). Most of the information on recent results is from the discoverers themselves. The following people all provided useful comments on earlier releases of this lexicon: David Bell, Nicolay Beluchenko, Johan Bontes, Scot Ellison, Nick Gotts, Dave Greene, Alan Hensel, Dean Hickerson, Dieter Leithner, Mark Niemiec, Gabriel Nivasch, Andrzej Okrasinski, Peter Rott, Tony Smith, Ken Takusagawa, Andrew Trevorrow and Malcolm Tyrrell. The format, errors, use of British English and anything else you might want to complain about are by Stephen Silver. COPYING This lexicon is copyright (C) Stephen Silver, 1997-2005. It may be freely copied and/or modified as long as due credit is given. This includes not just credit to those who have contributed in some way to the present version (see above), but also credit to those who have made any modifications. LEXICOGRAPHIC ORDER I have adopted the following convention: all characters (including spaces) other than letters and digits are ignored for the purposes of ordering the entries in this lexicon. (Many terms are used by some people as a single word, with or without a hyphen, and by others as two words. My convention means that I do not have to list these in two separate places. Indeed, I list them only once, choosing whichever form seems most common or sensible.) Digits lexicographically precede letters. FORMAT The format used in the ASCII version of this lexicon is loosely based on that of the Jargon File. In particular, the keywords are enclosed in colons and selected references to them are enclosed in curly brackets. The curly brackets will not be of much use unless you have a programmable text editor, in which case you could program it to jump from a reference to the corresponding definition when you hit a certain key. (The file lifelex.el, which you should have received with this lexicon, provides such a facility for GNU Emacs.) If you don't want the curly brackets you can safely remove them with two find and replace operations, since they are not used for any other purpose in this file. The colons are more generally useful. For example, a search for ":foo" will take you straight to the definition of the first word beginning with "foo" (or at least it would if there were any). The diagrams in this lexicon are in a very standard format. You should be able to simply copy a pattern, paste it into a new file and run it in your favourite Life program. If you use Johan Bontes' Life32, Mirek Wojtowicz' MCell or Andrew Trevorrow and Tomas Rokicki's Golly then you can, of course, paste the pattern directly into the Life program. If you view this lexicon in GNU Emacs and use lifelex.el then you should be able to load a pattern into your Life program with a single keypress, without needing to copy or paste. The diagrams use an asterisk to represent a live cell. If this looks ugly with the font you use then you can change to O or o with a global replace. I have restricted myself to diagrams of size 64x64 or less. Most definitions that have a diagram have also some data in brackets after the keyword. Oscillators are marked as pn (where n is a positive integer), meaning that the period is n (p1 indicates a still life). Wicks are marked in the same way but with the word "wick" added. For spaceships the speed (as a fraction of c, the speed of light), the direction and the period are given. Fuses are marked with speed and period and have the word "fuse" added. Wicks and fuses are infinite in extent and so have necessarily been truncated, with the ends stabilized wherever practical. SCOPE This lexicon covers only Conway's Life, and provides no information about other cellular automata. David Bell has written articles on two other interesting cellular automata: HighLife (which is similar to Life, but has a tiny replicator) and Day & Night (which is very different, but exhibits many of the same phenomena). These articles can be found on his web-site (http://www.canb.auug.org.au/~dbell/). ERRORS AND OMISSIONS If you find any errors (including typos) or serious omissions, then please let me know. NAMES When deciding whether to use full or abbreviated forms of forenames I have tried, wherever possible, to follow the usage of the person concerned. QUOTE Every other author may aspire to praise; the lexicographer can only hope to escape reproach. -- Samuel Johnson, 1775 DEDICATION This lexicon is dedicated to the memory of Dieter Leithner, who died on 26 February 1999. ----------------------------------------------------------------------- :101: (p5) Found by Achim Flammenkamp in August 1994. The name was suggested by Bill Gosper, noting that the {phase} shown below displays the period in binary. ....**......**.... ...*.*......*.*... ...*..........*... **.*..........*.** **.*.*..**..*.*.** ...*.*.*..*.*.*... ...*.*.*..*.*.*... **.*.*..**..*.*.** **.*..........*.** ...*..........*... ...*.*......*.*... ....**......**.... :1-2-3: (p3) Found by Dave Buckingham, August 1972. This is one of only three essentially different p3 {oscillator}s with only three cells in the {rotor}. The others are {stillater} and {cuphook}. ..**...... *..*...... **.*.**... .*.*..*... .*....*.** ..***.*.** .....*.... ....*..... ....**.... :1-2-3-4: (p4) See also {Achim's p4}. .....*..... ....*.*.... ...*.*.*... ...*...*... **.*.*.*.** *.*.....*.* ...*****... ........... .....*..... ....*.*.... .....*..... :14-ner: = {fourteener} :2 eaters: = {two eaters} :4-8-12 diamond: The following {pure glider generator}. ....****.... ............ ..********.. ............ ************ ............ ..********.. ............ ....****.... :4 boats: (p2) ...*.... ..*.*... .*.**... *.*..**. .**..*.* ...**.*. ...*.*.. ....*... :4F: = {Fast Forward Force Field} :Achim's p144: (p144) This was found (minus the blocks shown below) on a cylinder of width 22 by Achim Flammenkamp in July 1994. Dean Hickerson reduced it to a finite form using {figure-8}s the same day. The neater finite form shown here - replacing the figure-8s with blocks - was found by David Bell in August 1994. See {factory} for a use of this oscillator. **........................** **........................** ..................**........ .................*..*....... ..................**........ ..............*............. .............*.*............ ............*...*........... ............*..*............ ............................ ............*..*............ ...........*...*............ ............*.*............. .............*.............. ........**.................. .......*..*................. ........**.................. **........................** **........................** :Achim's p16: (p16) Found by Achim Flammenkamp, July 1994. .......**.... .......*.*... ..*....*.**.. .**.....*.... *..*......... ***.......... ............. ..........*** .........*..* ....*.....**. ..**.*....*.. ...*.*....... ....**....... :Achim's p4: (p4) Dave Buckingham found this in a less compact form (using two halves of {sombreros}) in 1976. The form shown here was found by Achim Flammenkamp in 1988. The {rotor} is two copies of the rotor of {1-2-3-4}, so the oscillator is sometimes called the "dual 1-2-3-4". ..**...**.. .*..*.*..*. .*.**.**.*. **.......** ..*.*.*.*.. **.......** .*.**.**.*. .*..*.*..*. ..**...**.. :Achim's p5: = {pseudo-barberpole} :Achim's p8: (p8) Found by Achim Flammenkamp, July 1994. .**...... *........ .*...*... .*...**.. ...*.*... ..**...*. ...*...*. ........* ......**. :acorn: (stabilizes at time 5206) A {methuselah} found by Charles Corderman. .*..... ...*... **..*** :A for all: (p6) Found by Dean Hickerson in March 1993. ....**.... ...*..*... ...****... .*.*..*.*. *........* *........* .*.*..*.*. ...****... ...*..*... ....**.... :against-the-grain grey ship: A {grey ship} in which the region of density 1/2 consists of lines of ON cells lying perpendicular to the direction in which the spaceship moves. See also {with-the-grain grey ship}. :agar: Any pattern covering the whole plane that is periodic in both space and time. The simplest (nonempty) agar is the {stable} one extended by the known {spacefiller}s. For some more examples see {chicken wire}, {houndstooth agar}, {onion rings}, {squaredance} and {Venetian blinds}. Tiling the plane with the pattern O......O produces another interesting example: a p6 agar which has a phase of {density} 3/4, which is the highest yet obtained for any phase of an oscillating pattern. :aircraft carrier: (p1) This is the smallest {still life} that has more than one {island}. **.. *..* ..** :airforce: (p7) Found by Dave Buckingham in 1972. The rotor consists of two copies of that used in the {burloaferimeter}. .......*...... ......*.*..... .......*...... .............. .....*****.... ....*.....*.** ...*.**...*.** ...*.*..*.*... **.*...**.*... **.*.....*.... ....*****..... .............. ......*....... .....*.*...... ......*....... :AK47 reaction: The following reaction (found by Rich Schroeppel and Dave Buckingham) in which a honey farm predecessor, catalysed by an eater and a block, reappears at another location 47 generations later, having produced a glider and a traffic light. This is the basis of a very small (but {pseudo}) p94 glider gun found by Paul Callahan in July 1994, and was in 1990 the basis for the Dean Hickerson's construction of the first {true} p94 gun. (This latter gun was enormous, and has now been superseded by comparatively small {Herschel loop} guns.) .....*.... ....*.*... ...*...*.. ...*...*.. ...*...*.. ....*.*... .....*.... .......... ..**...... ...*...... ***.....** *.......** :Al Jolson: = {Jolson} :almosymmetric: (p2) Found in 1971. ....*.... **..*.*.. *.*...... .......** .*....... *......*. **.*.*... .....*... :anteater: A pattern that consumes {ants}. :antlers: = {moose antlers} :ants: (p5 wick) The standard form is shown below. It is also possible for any ant to be displaced by one or two cells relative to either or both of its neighbouring ants. Dean Hickerson found {fencepost}s for both ends of this wick in October 1992 and February 1993. See {electric fence}, and also {wickstretcher}. **...**...**...**...**...**...**...**...**.. ..**...**...**...**...**...**...**...**...** ..**...**...**...**...**...**...**...**...** **...**...**...**...**...**...**...**...**.. :antstretcher: Any {wickstretcher} that stretches {ants}. :anvil: The following {induction coil}. .****. *....* .***.* ...*.** :APPS: (c/5 orthogonally, p30) An asymmetric {PPS}. The same as the {SPPS}, but with the two halves 15 generations out of phase with one another. Found by Alan Hensel in May 1998. :ark: A pair of mutually stabilizing {switch engine}s. The archetype is {Noah's ark}. The diagram below shows an ark found by Nick Gotts that takes until generation 736692 to stabilize, and can therefore be considered as a {methuselah}. ...........................*.... ............................*... .............................*.. ............................*... ...........................*.... .............................*** ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ **.............................. ..*............................. ..*............................. ...****......................... :arm: A long extension hanging off from the main body of a {spaceship} or {puffer} perpendicular to the direction of travel. A lot of known spaceships have multiple arms. This is an artefact of the search methods used to find such spaceships, rather than an indication of what a "typical" spaceship might look like. :ash: The ({stable} or oscillating) debris left by a random reaction. Experiments show that for random {soup}s with moderate initial densities (say 0.25 to 0.5) the resulting ash has a density of about 0.0287. (This is, of course, based on what happens in finite fields. In infinite fields the situation may conceivably be different in the long run because of the effect of certain initially very rare objects such as {replicator}s.) :aVerage: (p5) Found by Dave Buckingham, 1973. The average number of live {rotor} cells is five (V), which is also the period. ...**........ ....***...... ..*....*..... .*.****.*.... .*.*....*..*. **.***..*.*.* .*.*....*..*. .*.****.*.... ..*....*..... ....***...... ...**........ :B: = {B-heptomino} :B29: (c/4 diagonally, p4) The following {spaceship}, found by Hartmut Holzwart in September 2004. .......***....... .......*......... ***......*....... *......*.*....... .*....**.****.... ...****.*****.**. ....**.......**.* :B-52 bomber: The following p104 {double-barrelled} {glider} {gun}. It uses a {B-heptomino} and emits one glider every 52 generations. It was found by Noam Elkies in March 1996, except that Elkies used {blocker}s instead of {mold}s, the improvement being found by David Bell later the same month. .**.................................... .**.................*.................. ...................*.*............*.*.. ....................*............*..... **.......**.......................*..*. **.*.....**.......................*.*.* ...*.......................*.......*..* ...*.......................**.......**. *..*.................**.....*.......... .**..................*................. .....................***............... ....................................**. ....................................**. .**.................................... *..*................................... *.*.*................*.*....**.....**.. .*..*.................**....**.....**.* .....*............*...*...............* ..*.*............*.*..................* ..................*................*..* ....................................**. :babbling brook: Any {oscillator} whose {rotor} consists of a string of cells each of which is adjacent to exactly two other rotor cells, except for the endpoints which are adjacent to only one other rotor cell. Compare {muttering moat}. Examples include the {beacon}, the {great on-off}, the {light bulb} and the {spark coil}. The following less trivial example (by Dean Hickerson, August 1997) is the only one known with more than four cells in its rotor. It is p4 and has a 6-cell rotor. .......*........ .....***....**.. ....*...**..*... .*..*.**..*.*... *.*.*....**..**. .**..**....*.*.* ...*.*..**.*..*. ...*..**...*.... ..**....***..... ........*....... :backrake: Another term for a backwards {rake}. A p8 example by Jason Summers is shown below. See {total aperiodic} for a p12 example. .....***...........***..... ....*...*.........*...*.... ...**....*.......*....**... ..*.*.**.**.....**.**.*.*.. .**.*....*.**.**.*....*.**. *....*...*..*.*..*...*....* ............*.*............ **.......**.*.*.**.......** ............*.*............ ......***.........***...... ......*...*.........*...... ......*.*....***........... ............*..*....**..... ...............*........... ...........*...*........... ...........*...*........... ...............*........... ............*.*............ :backward glider: A {glider} which moves at least partly in the opposite direction to the {puffer}(s) or {spaceship}(s) under consideration. :baker: (c p4 fuse) A {fuse} by Keith McClelland. ..............** .............*.* ............*... ...........*.... ..........*..... .........*...... ........*....... .......*........ ......*......... .....*.......... ....*........... ...*............ ***............. .*.............. :baker's dozen: (p12) A {loaf} {hassle}d by two {block}s and two {caterer}s. The original form (using p4 and p6 oscillators to do the hassling) was found by Robert Wainwright in August 1989. **.........**.......... ****.*.....**.......... *.*..***............... ...........*........... ....**....*.*.......... ....*.....*..*....*.... ...........**....**.... ....................... ...............***..*.* ..........**.....*.**** ..........**.........** :bakery: (p1) A common formation of two bi-loaves. ....**.... ...*..*... ...*.*.... .**.*...*. *..*...*.* *.*...*..* .*...*.**. ....*.*... ...*..*... ....**.... :barberpole: Any p2 oscillator in the infinite sequence {bipole}, {tripole}, {quadpole}, {pentapole}, {hexapole}, {heptapole} ... (It wasn't my idea to suddenly change from Latin to Greek.) This sequence of oscillators was found by the MIT group in 1970. The term is also used (usually in the form "barber pole") to describe other {extensible} sections of oscillators or spaceships, especially those (usually of period 2) in which all generations look alike except for a translation and/or rotation/reflection. :barberpole intersection: = {quad} :barber's pole: = {barberpole} :barge: (p1) .*.. *.*. .*.* ..*. :basic shuttle: = {queen bee shuttle} :beacon: (p2) The third most common {oscillator}. Found by Conway, March 1970. **.. *... ...* ..** :beacon maker: (c p8 fuse) ..............** .............*.* ............*... ...........*.... ..........*..... .........*...... ........*....... .......*........ ......*......... .....*.......... ....*........... ...*............ ***............. ..*............. ..*............. :beehive: (p1) The second most common {still life}. .**. *..* .**. :beehive and dock: (p1) ...**. ..*..* ...**. ...... .****. *....* **..** :beehive on big table: = {beehive and dock} :beehive pusher: = {hivenudger} :beehive with tail: (p1) .**... *..*.. .**.*. ....*. ....** :belly spark: The spark of a {MWSS} or {HWSS} other than the {tail spark}. :bent keys: (p3) Found by Dean Hickerson, August 1989. See also {odd keys} and {short keys}. .*........*. *.*......*.* .*.**..**.*. ....*..*.... ....*..*.... :B-heptomino: (stabilizes at time 148) This is a very common pattern. It often arises with the cell at top left shifted one space to the left, which does not affect the subsequent evolution. B-heptominoes acquired particular importance in 1996 due to Dave Buckingham's work on {B track}s - see in particular {My Experience with B-heptominos in Oscillators}. *.** ***. .*.. :B-heptomino shuttle: = {twin bees shuttle} :bi-block: (p1) The smallest {pseudo still life}. **.** **.** :bi-boat: = {boat-tie} :biclock: The following {pure glider generator} consisting of two {clock}s. ..*.... **..... ..**... .*...*. ...**.. .....** ....*.. :big beacon: = {figure-8} :big fish: = {HWSS} :big glider: (c/4 diagonally, p4) This was found by Dean Hickerson in December 1989 and was the first known diagonal {spaceship} other than the {glider}. ...***............ ...*..***......... ....*.*........... **.......*........ *.*....*..*....... *........**....... .**............... .*..*.....*.**.... .*.........**.*... ...*.*......**..*. ....**.*....**...* ........*.......*. .......****...*.*. .......*.**...**** ........*...**.*.. .............**... .........*.***.... ..........*..*.... :big S: (p1) ....**. ...*..* ...*.** **.*... *..*... .**.... :big table: = {dock} :billiard table configuration: Any {oscillator} in which the {rotor} is enclosed within the {stator}. Examples include {airforce}, {cauldron}, {clock II}, {Hertz oscillator}, {negentropy}, {pinwheel}, {pressure cooker} and {scrubber}. :bi-loaf: This term has been used in at least three different senses. A bi-loaf can be half a {bakery}: .*..... *.*.... *..*... .**.*.. ...*.*. ...*..* ....**. or it can be the following much less common {still life}: ..*.... .*.*... *..*... .**.**. ...*..* ...*.*. ....*.. or the following {pure glider generator}: ..*. .*.* *..* .**. *..* *.*. .*.. :bipole: (p2) The {barberpole} of length 2. **... *.*.. ..... ..*.* ...** :bi-pond: (p1) .**.... *..*... *..*... .**.**. ...*..* ...*..* ....**. :bi-ship: = {ship-tie} :bit: A live {cell}. :biting off more than they can chew: (p3) Found by Peter Raynham, July 1972. *........... ***......... ...*........ ..**........ ...**....... ....**...... ...*..*..... ...*..**.... ....**.***.. ........*.*. ..........*. ..........** :Black&White: = {Immigration} :blasting cap: The {pi-heptomino} (after the shape at generation 1). A term used at MIT and still occasionally encountered. :blinker: (p2) The smallest and most common {oscillator}. Found by Conway, March 1970. *** :blinker puffer: Any {puffer} whose output is {blinker}s. However, the term is particularly used for p8 c/2 puffers. The first such blinker puffer was found by Robert Wainwright in 1984, and was unexpectedly simple: ...*..... .*...*... *........ *....*... *****.... ......... ......... ......... .**...... **.***... .****.... ..**..... ......... .....**.. ...*....* ..*...... ..*.....* ..******. Since then many more blinker puffers have been found. The following one was found by David Bell in 1992 when he was trying to extend an {x66}: .............***. ............***** ...........**.*** ............**... ................. ................. .........*.*..... ..*.....*..*..... .*****...*.*..... **...**.**....... .*.......*....... ..**..*..*....... ..........*...... ..**..*..*....... .*.......*....... **...**.**....... .*****...*.*..... ..*.....*..*..... .........*.*..... ................. ................. ............**... ...........**.*** ............***** .............***. The importance of this larger blinker puffer (and others like it), is that the engine which produces the blinker output is only p4. The blinker row produced by the puffer can easily be ignited, and burns cleanly with a speed of 2c/3. When the burning catches up to the engine, it causes a {phase change} in the puffer. This fact allows p8 blinker puffers to be used to construct rakes of all periods which are large multiples of four. :blinkers bit pole: (p2) Found by Robert Wainwright, June 1977. .....** ***.*.* ....... .*.*..* *....*. **...*. :blinker ship: A {growing spaceship} in which the wick consists of a line of {blinker}s. An example by Paul Schick based on his {Schick engine} is shown below. Here the front part is p12 and moves at c/2, while the back part is p26 and moves at 6c/13. Every 156 generations 13 blinkers are created and 12 are destroyed, so the wick becomes one blinker longer. ..........****............. ..........*...*............ ..........*................ .**........*..*............ **.**...................... .****...*.................. ..**...*.**........*....*** ......*...*........*....*.* ..**...*.**........*....*** .****...*.................. **.**...................... .**........*..*............ ..........*................ ..........*...*............ ..........****............. :block: (p1) The most common {still life}. ** ** :blockade: (p1) A common formation of four blocks. The final form of {lumps of muck}. **..................... **..................... ....................... ....................... .**.................**. .**.................**. ....................... ....................... .....................** .....................** :block and dock: (p1) ...**. ...**. ...... .****. *....* **..** :block and glider: (stabilizes at time 106) **.. *.*. ..** :blocker: (p8) Found by Robert Wainwright. See also {filter}. ......*.*. .....*.... **..*....* **.*..*.** ....**.... :block on big table: = {block and dock} :block on table: (p1) ..** ..** .... **** *..* :block pusher: A pattern emitting streams of {glider}s which can repeatedly push a block further away. This can be used as part of a {sliding block memory}. The following pattern, in which three gliders push a block one cell diagonally, is an example of how a block pusher works. ...................*.* ...................**. ....................*. ...................... ...................... ...................... ...*.................. ..*................... ..***................. ...................... ...................... ...................... ...................... **...*................ **...*.*.............. .....**............... :blom: (stabilizes at time 23314) The following {methuselah}, found by Dean Hickerson in July 2002. *..........* .****......* ..**.......* ..........*. ........*.*. :blonk: A {block} or a {blinker}. This term is mainly used in the context of {sparse Life} and was coined by Rich Schroeppel in September 1992. :blonker: (p6) The following {oscillator}, found by Nicolay Beluchenko in April 2004. *..**....*.. **..*.**.*.. ....*.*..... .....**..... .......*.... .......*...* .........*.* ..........*. :boat: (p1) The only 5-cell {still life}. **. *.* .*. :boat-bit: A binary digit represented by the presence of a {boat} next to a {snake} (or other suitable object, such as an {aircraft carrier}). The bit can be toggled by a {glider} travelling along a certain path. A correctly timed glider on a crossing path can detect whether the transition was from 1 to 0 (in which case the crossing glider is deleted) or from 0 to 1 (in which case it passes unharmed). Three gliders therefore suffice for a non-destructive read. The mechanisms involved are shown in the diagram below. Here the bit is shown in state 0. It is about to be set to 1 and then switched back to 0 again. The first crossing glider will survive, but the second will be destroyed. (In January 1997 David Bell found a method of reading the bit while setting it to 0. A {MWSS} is fired at the boat-bit. If it is already 0 then the MWSS passes unharmed, but if it is 1 then the boat and the MWSS are destroyed and, with the help of an {eater1}, converted into a glider which travels back along exactly the same path that is used by the gliders that toggle the boat-bit.) ......*.................. .......*................. .....***................. ......................... ......................... ......................... ......................... ......................... ......................... ......................... ................*........ ..............*.*........ ..........**...**........ ...........**............ ..........*..........*.** .....................**.* ......................... ......................... ......................... ......................... ......................... .*....................... .**...................... *.*...................... :boat maker: (c p4 fuse) ................** ...............*.* ..............*... .............*.... ............*..... ...........*...... ..........*....... .........*........ ........*......... .......*.......... ......*........... .....*............ *****............. ....*............. ....*............. ....*............. ....*............. :boat on boat: = {boat-tie} :boat-ship-tie: = {ship tie boat} :boatstretcher: See {tubstretcher}. :boat-tie: (p1) A 10-cell {still life} consisting of two {boat}s placed tip-to-tip. The name is a pun on "bow tie". .*.... *.*... .**... ...**. ...*.* ....*. :boojum reflector: (p1) Dave Greene's name for the following {reflector} which he found in April 2001, and which is currently the smallest known {stable} reflector. ....*.*......**............................. .....**......**............................. .....*...................................... ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ ........................................*... .......................................*.*.. .......................................*.*.. ....................**................**.**. ....................**...................... ......................................**.**. ..**..................................**.*.. .*.*.......................................* .*........................................** **.......................................... ............................................ ..................................**........ ..................................**....**.. ...........**...........................*.*. ..........*.*.............................*. ..........*...............................** .........**.......................**........ ..................................**........ ............................................ ............................................ .............................*.............. ............................*.*............. .............................*.............. :bookend: The following {induction coil}. It is generation 1 of {century}. ..** *..* ***. :bookends: (p1) **...** *.*.*.* ..*.*.. .**.**. :boss: (p4) Found by Dave Buckingham, 1972. .....*..... ....*.*.... ....*.*.... ...**.**... ..*.....*.. .*.*.*.*.*. .*.*...*.*. **.*...*.** *..*.*.*..* ..*.....*.. ...**.**... ....*.*.... ....*.*.... .....*..... :bottle: (p8) Found by Achim Flammenkamp in August 1994. The name is a back-formation from {ship in a bottle}. ....**......**.... ...*..*....*..*... ...*.*......*.*... .**..***..***..**. *......*..*......* *.**..........**.* .*.*..........*.*. ...**........**... .................. .................. ...**........**... .*.*..........*.*. *.**..........**.* *......*..*......* .**..***..***..**. ...*.*......*.*... ...*..*....*..*... ....**......**.... :bounding box: The smallest rectangular array of cells that contains the whole of a given pattern. For {oscillator}s and {gun}s this usually is meant to include all {phase}s of the pattern, but excludes, in the case of guns, the outgoing stream(s). :bow tie: = {boat-tie} :brain: (c/3 orthogonally, p3) Found by David Bell, May 1992. .***.........***. *.*.**.....**.*.* *.*.*.......*.*.* .*.**.**.**.**.*. .....*.*.*.*..... ...*.*.*.*.*.*... ..**.*.*.*.*.**.. ..***..*.*..***.. ..**..*...*..**.. .*....**.**....*. .*.............*. :breeder: Any pattern whose {population} grows at a quadratic rate, although it is usual to exclude {spacefiller}s. It is easy to see that this is the fastest possible growth rate. The term is also sometimes used to mean specifically the breeder created by Bill Gosper's group at MIT, which was the first known pattern exhibiting superlinear growth. There are four basic types of breeder, known as MMM, MMS, MSM and SMM (where M=moving and S=stationary). Typically an MMM breeder is a {rake} {puffer}, an MMS breeder is a puffer producing puffers which produce stationary objects ({still life}s and/or {oscillator}s), an MSM breeder is a {gun} puffer and an SMM breeder is a rake gun. There are, however, less obvious variants of these types. The original breeder was of type MSM (a p64 puffer puffing p30 glider guns). The known breeder with the smallest initial population is the {metacatacryst}. :bridge: A term used in naming certain {still life}s (and the {stator} part of certain {oscillator}s). It indicates that the object consists of two smaller objects joined edge to edge, as in {snake bridge snake}. :broken lines: A pattern constructed by Dean Hickerson in May 2005 which produces complex broken lines of gliders and blocks. :broth: = {soup} :BTC: = {billiard table configuration} :B track: A {track} for {B-heptomino}es. The term is more-or-less synonymous with {Herschel track}, since a B-heptomino becomes a Herschel plus a block in twenty generations. :buckaroo: A {queen bee shuttle} stabilized at one end by an eater in such a way that it can turn a glider, as shown below. This was found by Dave Buckingham in the 1970s. The name is due to Bill Gosper. ..*..................... *.*..................... .**..................... ...........*............ .........*.*............ ........*.*............. .......*..*...........** ........*.*...........** ...**....*.*............ ..*.*......*............ ..*..................... .**..................... :bullet heptomino: Generation 1 of the {T-tetromino}. .*. *** *** :bun: The following {induction coil}. By itself this is a common {predecessor} of the {honey farm}. See also {cis-mirrored R-bee}. .**. *..* .*** :bunnies: (stabilizes at time 17332) This is a {parent} of {rabbits} and was found independently by Robert Wainwright and Andrew Trevorrow. *.....*. ..*...*. ..*..*.* .*.*.... :burloaf: = {loaf} :burloaferimeter: (p7) Found by Dave Buckingham in 1972. See also {airforce}. ....**.... .....*.... ....*..... ...*.***.. ...*.*..*. **.*...*.* **.*....*. ....****.. .......... ....**.... ....**.... :bushing: That part of the {stator} of an {oscillator} which is adjacent to the {rotor}. Compare {casing}. :butterfly: The following pattern, or the formation of two beehives that it evolves into after 33 generations. (Compare {teardrop}, where the beehives are five cells closer together.) *... **.. *.*. .*** :by flops: (p2) Found by Robert Wainwright. ...*.. .*.*.. .....* *****. .....* .*.*.. ...*.. :c: = {speed of light} :CA: = {cellular automaton} :caber tosser: Any pattern whose {population} is asymptotic to c.log(t) for some constant c, and which contains a {glider} (or other {spaceship}) bouncing between a slower receding spaceship and a fixed {reflector} which emits a spaceship (in addition to the reflected one) whenever the bouncing spaceship hits it. As the receding spaceship gets further away the bouncing spaceship takes longer to complete each cycle, and so the extra spaceships emitted by the reflector are produced at increasingly large intervals. More precisely, if v is the speed of the bouncing spaceship and u the speed of the receding spaceship, then each interval is (v+u)/(v-u) times as long as the previous one. The population at time t is therefore n.log(t)/log((v+u)/(v-u)) + O(1), where n is the population of one of the extra spaceships (assumed constant). The first caber tosser was built by Dean Hickerson in May 1991. :Cambridge pulsar CP 48-56-72: = {pulsar} (The numbers refer to the populations of the three {phase}s. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.) :Canada goose: (c/4 diagonally, p4) Found by Jason Summers, January 1999. It consists of a {glider} plus a {tagalong}. ***.......... *.........**. .*......***.* ...**..**.... ....*........ ........*.... ....**...*... ...*.*.**.... ...*.*..*.**. ..*....**.... ..**......... ..**......... At the time of its discovery the Canada goose was the smallest known diagonal {spaceship} other than the glider, but this record has since been beaten, first by the second spaceship shown under {Orion}, and more recently by {quarter}. :candelabra: (p3) By Charles Trawick. See also the note under {cap}. ....**....**.... .*..*......*..*. *.*.*......*.*.* .*..*.****.*..*. ....*.*..*.*.... .....*....*..... :candlefrobra: (p3) Found by Robert Wainwright in November 1984. .....*.... .*.**.*.** *.*...*.** .*....*... .....**... The following diagram shows that a pair of these can act in some ways like {killer toads}. See also {snacker}. ....*...........*.... **.*.**.*...*.**.*.** **.*...*.*.*.*...*.** ...*....*...*....*... ...**...........**... ..................... ..................... .........***......... .........*..*........ .........*........... .........*...*....... .........*...*....... .........*........... ..........*.*........ :canoe: (p1) ...** ....* ...*. *.*.. **... :cap: The following {induction coil}. It can also be easily be stabilized to form a p3 oscillator - see {candelabra} for a slight variation on this. .**. *..* **** :carnival shuttle: (p12) Found by Robert Wainwright in September 1984 (using {MW emulator}s at the end, instead of the {monogram}s shown here). .................................*...* **...**..........................***** .*.*.*...*..*......**...*..*.......*.. .**.**..**...**....**..**...**....*.*. .*.*.*...*..*......**...*..*.......*.. **...**..........................***** .................................*...* :carrier: = {aircraft carrier} :casing: That part of the {stator} of an {oscillator} which is not adjacent to the {rotor}. Compare {bushing}. :catacryst: A 58-cell quadratic growth pattern found by Nick Gotts in April 2000. This was formerly the smallest known pattern with superlinear growth, but has since been superseded by the related {metacatacryst}. The catacryst consists of three {ark}s plus a glider-producing {switch engine}. It produces a block-laying switch engine every 47616 generations. Each block-laying switch engine has only a finite life, but the length of this life increases linearly with each new switch engine, so that the pattern overall grows quadratically, as an unusual type of MMS {breeder}. :catalyst: An object that participates in a reaction but emerges from it unharmed. The term is mostly applied to {still life}s, but can also be used of {oscillator}s, {spaceship}s, etc. The still lifes and oscillators which form a {conduit} are examples of catalysts. :caterer: (p3) Found by Dean Hickerson, August 1989. Compare with {jam}. In terms of its minimum {population} of 12 this is the smallest p3 {oscillator}. See also {double caterer} and {triple caterer}. ..*..... *...**** *...*... *....... ...*.... .**..... More generally, any oscillator which serves up a {bit} in the same manner may be referred to as a caterer. :Caterpillar: A {spaceship} that works by laying tracks at its front end. The only example constructed to date is a p270 17c/45 spaceship built by Gabriel Nivasch in December 2004, based on work by himself, Jason Summers and David Bell. This Caterpillar has a population of about 12 million in each generation and was put together by a computer program that Nivasch wrote. It is by far the largest and most complex Life object ever constructed. The 17c/45 Caterpillar is based on the following reaction between a {pi-heptomino} and a {blinker}: ...............* *.............** *............**. *.............** ...............* In this reaction, the pi moves forward 17 cells in the course of 45 generations, while the blinker moves back 6 cells and is rephased. This reaction has been known for many years, but it was only in September 2002 that David Bell suggested that it could be used to build a 17c/45 spaceship, based on a reaction he had found in which pis crawling along two rows of blinkers interact to emit a glider every 45 generations. Similar glider-emitting interactions were later found by Gabriel Nivasch and Jason Summers. The basic idea of the spaceship design is that streams of gliders created in this way can be used to construct fleets of {standard spaceship}s which convey gliders to the front of the blinker tracks, where they can be used to build more blinkers. A different Caterpillar may be possible based on the following reaction, in which the pattern at top left reappears after 31 generations displaced by (13,1), having produced a new NW-travelling glider. In this case the tracks would be waves of backward-moving gliders. .**..................... ...*.................... ...*.**................. ***....*................ .......*................ .....***................ ........................ ........................ ........................ ........................ ........................ ........................ .....................*** .....................*.. ......................*. :Catherine wheel: = {pinwheel} :cauldron: (p8) Found in 1971 independently by Don Woods and Robert Wainwright. Compare with {Hertz oscillator}. .....*..... ....*.*.... .....*..... ........... ...*****... *.*.....*.* **.*...*.** ...*...*... ...*...*... ....***.... ........... ....**.*... ....*.**... :cavity: = {eater plug} :cell: The fundamental unit of space in the Life universe. The term is often used to mean a live cell - the sense is usually clear from the context. :cellular automaton: A certain class of mathematical objects of which {Life} is an example. A cellular automaton consists of a number of things. First there is a positive integer n which is the dimension of the cellular automaton. Then there is a finite set of states S, with at least two members. A state for the whole cellular automaton is obtained by assigning an element of S to each point of the n-dimensional lattice Z^n (where Z is the set of all integers). The points of Z^n are usually called cells. The cellular automaton also has the concept of a neighbourhood. The neighbourhood N of the origin is some finite (nonempty) subset of Z^n. The neighbourhood of any other cell is obtained in the obvious way by translating that of the origin. Finally there is a transition rule, which is a function from S^N to S (that is to say, for each possible state of the neighbourhood the transition rule specifies some cell state). The state of the cellular automaton evolves in discrete time, with the state of each cell at time t+1 being determined by the state of its neighbourhood at time t, in accordance with the transition rule. There are some variations on the above definition. It is common to require that there be a quiescent state, that is, a state such that if the whole universe is in that state at generation 0 then it will remain so in generation 1. (In Life the OFF state is quiescent, but the ON state is not.) Other variations allow spaces other than Z^n, neighbourhoods that vary over space and/or time, probabilistic or other non-deterministic transition rules, etc. It is common for the neighbourhood of a cell to be the 3x...x3 (hyper)cube centred on that cell. (This includes those cases where the neighbourhood might more naturally be thought of as a proper subset of this cube.) This is known as the Moore neighbourhood. :centinal: (p100) Found by Bill Gosper. This combines the mechanisms of the p46 and p54 shuttles (see {twin bees shuttle} and {p54 shuttle}). **................................................** .*................................................*. .*.*.....................**.....................*.*. ..**........*............**............**.......**.. ...........**..........................*.*.......... ..........**.............................*.......... ...........**..**......................***.......... .................................................... .................................................... .................................................... ...........**..**......................***.......... ..........**.............................*.......... ...........**..........................*.*.......... ..**........*............**............**.......**.. .*.*.....................**.....................*.*. .*................................................*. **................................................** :century: (stabilizes at time 103) This is a common pattern which evolves into three {block}s and a {blinker}. In June 1996 Dave Buckingham built a neat p246 glider {gun} using a century as the engine. See also {bookend} and {diuresis}. ..** ***. .*.. :chemist: (p5) .......*....... .......***..... ..........*.... .....***..*..** ....*.*.*.*.*.* ....*...*.*.*.. .**.*.....*.**. ..*.*.*...*.... *.*.*.*.*.*.... **..*..***..... ....*.......... .....***....... .......*....... :C-heptomino: Name given by Conway to the following {heptomino}, a less common variant of the {B-heptomino}. .*** ***. .*.. :Cheshire cat: A block {predecessor} by C. R. Tompkins that unaccountably appeared both in Scientific American and in {Winning Ways}. See also {grin}. .*..*. .****. *....* *.**.* *....* .****. :chicken wire: A type of {stable} {agar} of {density} 1/2. The simplest version is formed from the tile: **.. ..** But the "wires" can have length greater than two and need not all be the same. For example: **...****..... ..***....***** :cigar: = {mango} :cis-beacon on anvil: (p2) ...**. ....*. .*.... .**... ...... .****. *....* .***.* ...*.** :cis-beacon on table: (p2) ..** ...* *... **.. .... **** *..* :cis-boat with tail: (p1) .*... *.*.. **.*. ...*. ...** :cis fuse with two tails: (p1) See also {pulsar quadrant}. ...*.. .***.. *...** .*..*. ..*.*. ...*.. :cis-mirrored R-bee: (p1) .**.**. *.*.*.* *.*.*.* .*...*. :cis snake: = {canoe} :clean: Opposite of {dirty}. A reaction which produces a small number of different products which are desired or which are easily deleted is said to be clean. For example, a {puffer} which produces just one object per period is clean. Clean reactions are useful because they can be used as building blocks in larger constructions. When a {fuse} is said to be clean, or to burn cleanly, this usually means that no debris at all is left behind. :clock: (p2) Found by Simon Norton, May 1970. This is the fifth or sixth most common {oscillator}, being about as frequent as the {pentadecathlon}, but much less frequent than the {blinker}, {toad}, {beacon} or {pulsar}. But it's surprisingly rare considering its small size. ..*. *.*. .*.* .*.. :clock II: (p4) Compare with {pinwheel}. ......**.... ......**.... ............ ....****.... **.*....*... **.*..*.*... ...*..*.*.** ...*.*..*.** ....****.... ............ ....**...... ....**...... :cloud of smoke: = {smoke} :cloverleaf: This name was given by Robert Wainwright to his p2 oscillator {washing machine}. But Achim Flammenkamp also gave this name to {Achim's p4}. :cluster: Any pattern in which each live cell is connected to every other live cell by a path that does not pass through two consecutive dead cells. This sense is due to Nick Gotts, but the term has also been used in other senses, often imprecise. :CNWH: Conweh, creator of the Life universe. :Coe ship: (c/2 orthogonally, p16) A {puffer engine} discovered by Tim Coe in October 1995. ....****** ..**.....* **.*.....* ....*...*. ......*... ......**.. .....****. .....**.** .......**. :Coe's p8: (p8) Found by Tim Coe in August 1997. **.......... **..**...... .....**..... ....*..*.... .......*..** .....*.*..** :colorized Life: A {cellular automaton} which is the same as Life except for the use of a number of different ON states ("colours"). All ON states behave the same for the purpose of applying the Life rule, but additional rules are used to specify the colour of the resulting ON cells. Examples are {Immigration} and {QuadLife}. :colour of a glider: The colour of a {glider} is a property of the glider which remains constant while the glider is moving along a straight path, but which can be changed when the glider bounces off a {reflector}. It is an important consideration when building something using reflectors. The colour of a glider can be defined as follows. First choose some cell to be the origin. This cell is then considered to be white, and all other cells to be black or white in a checkerboard pattern. (So the cell with coordinates (m,n) is white if m+n is even, and black otherwise.) Then the colour of a glider is the colour of its leading cell when it is in a phase which can be rotated to look like this: *** ..* .*. A reflector which does not change the colour of gliders obviously cannot be used to move a glider onto a path of different colour than it started on. But a 90-degree reflector which does change the colour of gliders is similarly limited, as the colour of the resulting glider will depend only on the direction of the glider, no matter how many reflectors are used. For maximum flexibility, therefore, both types of reflector are required. :complementary blinker: = {fore and back} :compression: = {repeat time} :conduit: Any arrangement of {still life}s and/or {oscillator}s which move an active object to another location, perhaps also transforming it into a different active object at the same time, but without leaving any permanent debris (except perhaps gliders, or other spaceships) and without any of the still lifes or oscillators being permanently damaged. Probably the most important conduit is the following remarkable one (Dave Buckingham, July 1996) in which a {B-heptomino} is transformed into a {Herschel} in 59 generations. .........**.* *.**......*** **.*.......*. ............. .........**.. .........**.. :confused eaters: (p4) Found by Dave Buckingham before 1973. *.......... ***........ ...*....... ..*........ ..*..*..... .....*..... ...*.*..... ...**..**.. .......*.*. .........*. .........** :converter: A {conduit} in which the input object is not of the same type as the output object. This term tends to be preferred when either the input object or the output object is a {spaceship}. The following diagram shows a p8 {pi-heptomino}-to-{HWSS} converter. This was originally found by Dave Buckingham in a larger form (using a {figure-8} instead of the {boat}). The improvement shown here is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) {oscillator}s of periods 44, 46 and 60 to replace the {Kok's galaxy}. .*.*..*........ .***.*.**...... *......*.....*. .*.....**...*.* .............** **.....*....... .*......*...... **.*.***....... ..*..*.*....... ............*** ............*.* ............*.* :convoy: A collection of {spaceship}s all moving in the same direction at the same speed. :Corder-: Prefix used for things involving {switch engine}s, after Charles Corderman. :Corder engine: = {switch engine} :Cordergun: A {gun} firing {Cordership}s. The first was built by Jason Summers in July 1999, using a {glider synthesis} by Stephen Silver. :Cordership: Any {spaceship} based on {switch engine}s. These necessarily move at a speed of c/12 diagonally with a period of 96 (or a multiple thereof). The first was found by Dean Hickerson in April 1991. Corderships are the slowest spaceships so far constructed, although arbitrarily slow spaceships are known to exist (see {universal constructor}). Hickerson's original Cordership used 13 switch engines. He soon reduced this to 10, and in August 1993 to 7. In July 1998 he reduced it to 6. In January 2004, Paul Tooke found the 3-engine Cordership shown below. ................................**.*........................... ...............................***.*......*.*.................. ..............................*....*.*....*.................... ...............................**......*.*...*................. ................................*...*..*..**................... ...................................*.**...*.................... ..................................*.*................**........ ..................................*.*................**........ ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... .............................................................** ....................................................**.......** .......................................*.........*.****........ ..................................*...*****.....**.*...**...... .................................*.*.......**....*..**.**...... .................................*.......*.**.....******....... ..................................*........**......*........... ...................................*...****.................... ........................................***.................... ........................*.*.........**......................... ........................*.*.*......*.*......................... .......................*..**.*....**........................... ........................**...*.*.**.*.......................... ........................**...**.*****.......................... ............................*.**...**.......................... ...........................*.*................................. ..**.*......................................................... .***.*......*.*................................................ *....*.*....*.................................................. .**......*.*...*............................................... ..*...*..*..**...........*..................................... .....*.**...*...........***.................................... ....*.*.................*..*................................... ....*.*................*....*.................................. ........................*...................................... ............................................................... ........................*..*................................... .........................*.*................................... ............................................................... .....................*......................................... ....................***........................................ ...................**.**....................................... .........*........**.*.....*................................... ....*...*****....**......**.................................... ...*.*.......**..**.......**................................... ...*.......*.**................................................ ....*........**................................................ .....*...****.................................................. ..........***.................................................. ............................................................... ............................................................... ............................................................... ...........**.................................................. ...........**.................................................. :cousins: (p3) This contains two copies of the {stillater} {rotor}. .....*.**.... ...***.*.*... *.*......*... **.**.**.*.** ...*.*....*.* ...*.*.***... ....**.*..... :cover: The following {induction coil}. See {scrubber} for an example of its use. ....* ..*** .*... .*... **... :covered table: = {cap} :cow: (c p8 fuse) **.......**..**..**..**..**..**..**..**..**..**..**..**..... **....*.***..**..**..**..**..**..**..**..**..**..**..**...** ....**.*.................................................*.* ....**...*************************************************.. ....**.*..................................................*. **....*.***..**..**..**..**..**..**..**..**..**..**..**..**. **.......**..**..**..**..**..**..**..**..**..**..**..**..... :CP pulsar: = {pulsar} :crane: (c/4 diagonally, p4) The following {spaceship} found by Nicolay Beluchenko in September 2005, a minor modification of a {tubeater} found earlier by Hartmut Holzwart. The wing is of the same form as in the {swan} and {Canada goose}. .**................. **.................. ..*................. ....**...*.......... ....**..*.*......... .......**.*......... .......**........... .......**........... .................**. .........*....**.*.. .........***..**.... .........***..**.... ..........**........ .................... ............*....... ...........**....... ...........*........ ............*....... .................... .............**..... ..............*.**.. ..................*. ...............**... ...............**... .................*.. ..................** :cross: (p3) Found by Robert Wainwright in October 1989. ..****.. ..*..*.. ***..*** *......* *......* ***..*** ..*..*.. ..****.. In February 1993, Hartmut Holzwart noticed that this is merely the smallest of an infinite family of p3 oscillators. The next smallest member is shown below. ..****.****.. ..*..*.*..*.. ***..***..*** *...........* *...........* ***.......*** ..*.......*.. ***.......*** *...........* *...........* ***..***..*** ..*..*.*..*.. ..****.****.. :crowd: (p3) Found by Dave Buckingham in January 1973. ...........*.. .........***.. .....**.*..... .....*...*.... .......**.*... ...****...*... *.*.....*.*.** **.*.*.....*.* ...*...****... ...*.**....... ....*...*..... .....*.**..... ..***......... ..*........... :crown: The p12 part of the following p12 {oscillator}, where it is {hassle}d by {caterer}, a {jam} and a {HW emulator}. This oscillator was found by Noam Elkies in January 1995. ..........*........... ..........*......*.... ...*....*...*...**.... ...**....***.......... .........***..***..*.* .*..***.........*.**** *.*.*...............** *..*.................. .**........**......... ......**.*....*.**.... ......*..........*.... .......**......**..... ....***..******..***.. ....*..*........*..*.. .....**..........**... :crucible: = {cauldron} :crystal: A regular growth that is sometimes formed when a stream of {glider}s, or other {spaceship}s, is fired into some junk. The most common example is initiated by the following collision of a glider with a {block}. With a glider stream of even {period} at least 82, this gives a crystal which forms a pair {beehive}s for every 11 gliders which hit it. .*...... ..*...** ***...** :cuphook: (p3) Found by Rich Schroeppel, October 1970. This is one of only three essentially different p3 {oscillator}s with only three cells in the {rotor}. The others are {1-2-3} and {stillater}. ....**... **.*.*... **.*..... ...*..... ...*..*.. ....**.*. .......*. .......** The above is the original form, but it can be made more compact: ....**. ...*.*. ...*... **.*... **.*..* ...*.** ...*... ..**... :curl: = {loop} :dart: (c/3 orthogonally, p3) Found by David Bell, May 1992. .......*....... ......*.*...... .....*...*..... ......***...... ............... ....**...**.... ..*...*.*...*.. .**...*.*...**. *.....*.*.....* .*.**.*.*.**.*. :dead spark coil: (p1) Compare {spark coil}. **...** *.*.*.* ..*.*.. *.*.*.* **...** :de Bruijn diagram: = {de Bruijn graph} :de Bruijn graph: As applied to Life, a de Bruijn graph is a graph showing which pieces can be linked to which other pieces to form a valid part of a Life pattern of a particular kind. For example, if we are interested in {still life}s, then we could consider 2x3 rectangular pieces and the de Bruijn graph would show which pairs of these can be overlapped to form 3x3 squares in which the centre cell remains unchanged in the next generation. David Eppstein's search program {gfind} is based on de Bruijn graphs. :Deep Cell: A pattern by Jared James Prince, based on David Bell's {unit Life cell}, in which each unit cell simulates two Life cells, in such a way that a Life universe filled with Deep Cells simulates two independent Life universes running in parallel. In fact, a Life universe filled with Deep Cells can simulate infinitely many Life universes, as follows. Let P_1, P_2, P_3, ... be a sequence of Life patterns. Set the Deep Cells to run a simulation of P_1 in parallel with a simulation of a universe filled with Deep Cells, with these simulated Deep Cells running a simulation of P_2 in parallel with another simulation of a universe filled with Deep Cells, with these doubly simulated Deep Cells simulating P_3 in parallel with yet another universe of Deep Cells, and so on. Deep Cell is available from {http://psychoticdeath.com/life.htm}. :density: The density of a pattern is the limit of the proportion of live cells in a (2n+1)x(2n+1) square centred on a particular cell as n tends to infinity, when this limit exists. (Note that it does not make any difference what cell is chosen as the centre cell. Also note that if the pattern is finite then the density is zero.) There are other definitions of density, but this one will do here. In 1994 Noam Elkies proved that the maximum density of a stable pattern is 1/2, which had been the conjectured value. See the paper listed in the bibliography. Marcus Moore provided a simpler proof in 1995, and in fact proves that a {still life} with an m x n {bounding box} has at most (mn+m+n)/2 cells. But what is the maximum average density of an oscillating pattern? The answer is conjectured to be 1/2 again, but this remains unproved. The best upper bound so far obtained is 8/13 (Hartmut Holzwart, September 1992). The maximum possible density for a {phase} of an oscillating pattern is also unknown. An example with a density of 3/4 is known (see {agar}), but densities arbitrarily close to 1 may perhaps be possible. :D-heptomino: = {Herschel} :diamond: = {tub} :diamond ring: (p3) Found by Dave Buckingham in 1972. ......*...... .....*.*..... ....*.*.*.... ....*...*.... ..**..*..**.. .*....*....*. *.*.**.**.*.* .*....*....*. ..**..*..**.. ....*...*.... ....*.*.*.... .....*.*..... ......*...... :diehard: Any pattern that vanishes, but only after a long time. The following example vanishes in 130 generations, which is probably the limit for patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells - e.g., for 8 cells we could have a glider heading towards an arbitrarily distant blinker. ......*. **...... .*...*** :dinner table: (p12) Found by Robert Wainwright in 1972. .*........... .***.......** ....*......*. ...**....*.*. .........**.. ............. .....***..... .....***..... ..**......... .*.*....**... .*......*.... **.......***. ...........*. :dirty: Opposite of {clean}. A reaction which produces a large amount of complicated junk which is difficult to control or use is said to be dirty. Many basic {puffer engine}s are dirty and need to be {tame}d by accompanying {spaceship}s in order to produce clean output. :diuresis: (p90) Found by David Eppstein in October 1998. His original stabilization used {pentadecathlon}s. The stabilization with complicated {still life}s shown here (in two slightly different forms) was found by Dean Hickerson the following day. The name is due to Bill Gosper (see {kidney}). .....**................**.... ......*................*..... ......*.*............*.*..... .......**............**...... ............................. ....**..................**... ....*.*..........**....*.*... .....*..........*.*.....*.... ..*.............**.........*. ..******........*.....******. .......*..............*...... ....**..................**... ....*....................*... .....*..................*.... ..***..*..............*..***. ..*..***........*.....***...* ...*............**.......***. ....**..........*.*.....*.... ......*..........**....*..**. ....**..................**.*. .*..*....................*... *.*.*..**............**..*... .*..*.*.*............*.*.**.. ....*.*................*..*.. .....**................**.... :dock: The following {induction coil}. .****. *....* **..** :domino: The 2-cell {polyomino}. A number of objects, such as the {HWSS} and {pentadecathlon}, produce domino {spark}s. :do-see-do: The following reaction, found by David Bell in 1996, in which two {glider}s appear to circle around each other as they are reflected 90 degrees by a {twin bees shuttle}. Four copies of the reaction can be used to create a p92 glider loop which repeats the do-see-do reaction forever. .....................................................*.* .....................................................**. ......................................................*. ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ................................................**...... ................................................*....... ..............................................*.*....... ..............................................**........ ..............................*.*....................... ..............................**........................ ...............................*........................ ........................................................ .......................***.............................. **........***........**.*.**............................ **........*...*.....*.....**............................ ..........*....*.....**.*.**............................ ...........*...*.......***.............................. ........................................................ ...........*...*........................................ ..........*....*........................................ **........*...*............**........................... **........***..............**........................... :double-barrelled: Of a {gun}, emitting two streams of {spaceship}s (or {rake}s). See {B-52 bomber} for an example. :double block reaction: A certain reaction that can be used to stabilize the {twin bees shuttle} (qv). This was discovered by David Bell in October 1996. The same reaction sometimes works in other situations, as shown in the following diagram where a pair of blocks eats an {R-pentomino} and a {LWSS}. (The LWSS version was known at least as early 1994, when Paul Callahan saw it form spontaneously as a result of firing a LWSS stream at some random junk.) .****.....**.... *...*......**.** ....*......*..** *..*............ ................ .............**. .............**. :double caterer: (p3) Found by Dean Hickerson, October 1989. Compare {caterer} and {triple caterer}. .....**...*........ ....*..*..***...... ....**.*.....*..... ......*.****.*..... ..***.*.*...*.**... .*..*..*...*..*.*.. *.*..*...*.**....*. .*..........**.***. ..**.**.**...*..... ...*...*.....*.***. ...*...*......**..* .................** :double ewe: (p3) Found by Robert Wainwright before September 1971. ......**............ .......*............ ......*............. ......**............ .........**......... ......***.*......... *.**.*.............. **.*.*.............. .....*...*.......... ....*...**....**.... ....**....**...*.... ..........*...*..... ..............*.*.** ..............*.**.* .........*.***...... .........**......... ............**...... .............*...... ............*....... ............**...... :double wing: = {moose antlers} :dove: The following {induction coil}. .**.. *..*. .*..* ..*** :down boat with tail: = {cis-boat with tail} :dragon: (c/6 orthogonally, p6) This {spaceship}, discovered by Paul Tooke in April 2000, was the first known c/6 spaceship. All other known orthogonal c/6 spaceships are {flotilla}s involving at least two dragons. .............*..**......*..*** .....*...****.******....*..*** .*****....*....*....***....... *......**.*......**.***..*.*** .*****.***........****...*.*** .....*..*..............*...... ........**..........**.**..... ........**..........**.**..... .....*..*..............*...... .*****.***........****...*.*** *......**.*......**.***..*.*** .*****....*....*....***....... .....*...****.******....*..*** .............*..**......*..*** :drain trap: = {paperclip} :drifter: A perturbation moving within a stable pattern. Dean Hickerson has written a program to search for drifters, with the hope of finding one which could be moved around a track. Because drifters can be very small, they could be packed more tightly than {Herschel}s, and so allow the creation of {oscillator}s of periods not yet attained, and possibly prove that Life is {omniperiodic}. Hickerson has found a number of components towards this end, but it has proved difficult to change the direction of movement of a drifter, and so far no complete track has been found. However, Hickerson has had success using the same search program to find {eater}s with novel properties, such as that used in {diuresis}. :dual 1-2-3-4: = {Achim's p4} :early universe: Conway's somewhat confusing term for {sparse Life}. :eater: Any {still life} that has the ability to interact with certain patterns without suffering any permanent damage. (If it doesn't suffer even temporary damage then it may be referred to as a {rock}.) The {eater1} is a very common eater, and the term "eater" is often used specifically for this object. Other eaters include {eater2}, {eater3}, {eater4} and even the humble {block}. (In fact the block was the first known eater, being found capable of eating beehives from a {queen bee}.) Another useful eater is shown below, feasting on a glider. ...*..... ...*.*... ...**.... ......... .......** ...*...** ..*.*.... .*.*..... .*....... **....... :eater1: (p1) Usually simply called an {eater}, and also called a fishhook. Its ability to eat various objects was discovered by Bill Gosper in 1971. **.. *.*. ..*. ..** :eater2: (p1) This {eater} was found by Dave Buckingham in the 1970s. Mostly it works like the ordinary eater (see {eater1}) but with two slight differences that make it useful despite its size: it takes longer to recover from each bite and it acts like an eater in two directions. The first property means that, among other things, it can eat a {glider} in a position that would destroy a fishhook. This novel glider-eating action is occasionally of use in itself, and combined with the symmetry means that an eater2 can eat gliders along four different paths. ...*.** .***.** *...... .***.** ...*.*. ...*.*. ....*.. The following eater2 variant (Stephen Silver, May 1998) can be useful for obtaining smaller {bounding box}es. A more compact variant with the same purpose can be seen under {gliderless}. **.... *..... ..*.** .**.** ...... .**.** ..*.*. ..*.*. ...*.. :eater3: (p1) This large symmetric {eater}, found by Dave Buckingham, has a very different eating action from the {eater1} and {eater2}. The {loaf} can take bites out things, being flipped over in the process. The rest of the object merely flips it back again. .........**. ....**..*..* .*..*....*.* *.*.*.....*. .*..*.**.... ....*..*.... .....*....*. ......*****. ............ ........*... .......*.*.. ........*... :eater4: (p1) Another {eater} by Dave Buckingham, which he found in 1971, but did not recognize as an eater until 1975 or 1976. It can't eat {glider}s, but it can be used for various other purposes. The four NE-most centre cells regrow in a few generations after being destroyed by taking a bite out of something. ...**......... ...*.......... **.*.......... *..**......... .**....*...... ...*****...... ...*....**.... ....**..*..... ......*.*..... ......*.*.*..* .......**.**** .........*.... .........*.*.. ..........**.. :eater/block frob: (p4) Found by Dave Buckingham in 1976 or earlier. .**....... ..*....... ..*.*..... ...*.*.... .....**.** ........** ..**...... ...*...... ***....... *......... :eater-bound pond: = {biting off more than they can chew} :eater-bound Z-hexomino: = {pentoad} :eater eating eater: = {two eaters} :eater plug: (p2) Found by Robert Wainwright, February 1973. .......* .....*** ....*... .....*.. ..*..*.. .*.**... .*...... **...... :eaters +: = {French kiss} :eaters plus: = {French kiss} :ecologist: (c/2 orthogonally, p20) This consists of the classic {puffer train} with a {LWSS} added to suppress the debris. See also {space rake}. ****.....**........ *...*...**.**...... *........****...... .*..*.....**....... ................... .....*.........**.. ...***........***** ..*...*.....*....** ..*....*****.....** ..**.*.****....**.. ....*...**.***..... .....*.*........... ................... ................... ****............... *...*.............. *.................. .*..*.............. :edge-repair spaceship: A {spaceship} which has an edge that possesses no {spark} and yet is able to {perturb} things because of its ability to repair certain types of damage to itself. The most useful examples are the following two small p3 c/3 spaceships: ..................................*..... ........*.......................***.***. .......****....................**......* ..*...*...**.**...........*...*..*...**. .****.....*..**..........****........... *...*.......*..*........*...*........... .*.*..*..................*.*..*......... .....*.......................*.......... These were found by David Bell in 1992, but the usefulness of the edge-repair property wasn't recognised until July 1997. The following diagram (showing an edge-repair spaceship deleting a {Herschel}) demonstrates the self-repairing action. ................*....... *..............****..... *.*.......*...*...**.**. ***......****.....*..**. ..*.....*...*.......*..* .........*.*..*......... .............*.......... In October 2000, David Bell found that a {T-tetromino} component of a c/4 spaceship can also be self-repairing. Stephen Silver noticed that it could be used to delete beehives and, in November 2000, found the smallest known c/4 spaceship with this edge-repair component - in fact, two copies of the component: .**.......................... *..*......................... .**.......................... ............................. .......*.*................... .......*..................... .......*.*..*..*............. ..........*.................. ...........*.**.*............ ............***.*............ ...........*....*..*.**...... ........*...**...*.****...... ........**..*..*.**....*....* ........*........**....*..*** .............**...**...*..**. .**.......................... *..*......................... .**.......................... :edge shooter: A {gun} which fires its gliders (or whatever) right at the edge of the pattern, so that it can be used to fire them closely parallel to others. This is useful for constructing complex guns. Compare {glider pusher}, which can in fact be used for making edge shooters. The following diagram shows a p46 edge shooter found by Paul Callahan in June 1994. **............**..*....**..**............. **............*.**......**.**............. ...............*......*.*................. ...............***....**.................. .......................................... ...............***....**.................. ...............*......*.*................. **............*.**......**................ **............**..*....**................. .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... ...............................***...***.. ..............................*...*.*...*. .............................*...**.**...* .............................*.**.....**.* ...............................*.......*.. .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... ...............................**.....**.. ...............................**.....**.. :edge spark: A {spark} at the side of a {spaceship} that can be used to {perturb} things as the spaceship passes by. :edge sparker: A {spaceship} that produces one or more {edge spark}s. :egg: = {non-spark} :E-heptomino: Name given by Conway to the following {heptomino}. .*** **.. .**. :elbow ladder: Scot Ellison's name for the type of pattern he created in which one or more {glider}s shuttle back and forth (using the {kickback reaction}) deleting the output gliders from a pair of {slide gun}s. :electric fence: (p5) A stabilization of {ants}. Dean Hickerson, February 1993. ..........*.................................................. .........*.*........................**....................... ..*....***.*.....*...................*...*..*......*.....**.. .*.*..*....**...*.*..................*.***..***...*.*....*... .*.*..*.**.......*....................*...**...*.*..*......*. **.**.*.*.*****.....*..................**...*..*.*.**.**..**. .*.*..*...*..*..*.......**...**...**....**.**..*.*..*.*.*.... .*..**....**......***.**...**...**...***.....****.***.*...**. ..*..***..*..*.****...**...**...**...***.**..*....*.*....*..* ...**...*.*..*.....**...**...**...**......*............*...** .....**.*.**.*.**..*......................*........**.*...... .....*.**.*..*.**....*.................**.*.*................ ...........**.......**..................*..**................ ......................................*.*.................... ......................................**..................... :elevener: (p1) **.... *.*... ..*... ..***. .....* ....** :Elkies' p5: (p5) Found by Noam Elkies in 1997. .*....... *..***... ..*...... ...*.*..* ..**.**** ....*.... ....*.*.. .....**.. :emu: Dave Buckingham's term for a {Herschel loop} that does not emit {glider}s (and so is "flightless"). All known Herschel loops of periods 57, 58, 59 and 61 are emus. See also {Quetzal}. :emulator: Any one of three p4 oscillators that produce {spark}s similar to those produced by {LWSS}, {MWSS} and {HWSS}. See {LW emulator}, {MW emulator} and {HW emulator}. Larger emulators are also possible, but they require stabilizing objects to suppress their {non-spark}s and so are of little use. The emulators were discovered by Robert Wainwright in June 1980. :engine: The active portion of an object (usually a {puffer} or {gun}) which is considered to actually produce its output, and which generally permits no variation in how it works. The other parts of the object are just there to support the engine. For examples, see {puffer train}, {Schick engine}, {blinker puffer}, {frothing puffer} and {line puffer}. :en retard: (p3) Found by Dave Buckingham, August 1972. .....*..... ....*.*.... **.*.*.*.** .*.*...*.*. *..*.*.*..* .**.....**. ...**.**... ...*.*.*... ....*.*.... ..*.*.*.*.. ..**...**.. :Enterprise: (c/4 diagonally, p4) Found by Dean Hickerson, March 1993. .......***........... .....*.**............ ....****............. ...**.....*.......... ..***..*.*.*......... .**...*.*..*......... .*.*.*****........... **.*.*...*........... *........**.......... .**..*...*.*......... ....**..*.**......*.. ...........**.....*** ............*..***..* ............*..*..**. .............*.**.... ............**....... ............**....... ...........*......... ............*.*...... ...........*..*...... .............*....... :Eureka: (p30) A {pre-pulsar} {shuttle} found by Dave Buckingham in August 1980. A variant is obtained by shifting the top half two spaces to either side. .*..............*. *.*....*.......*.* .*...**.**......*. .......*.......... .................. .................. .................. .......*.......... .*...**.**......*. *.*....*.......*.* .*..............*. :evolutionary factor: For an unstable pattern, the time to stabilization divided by the initial {population}. For example, the {R-pentomino} has an evolutionary factor of 220.6, while {bunnies} has an evolutionary factor of 1925.777... The term is no longer in use. :exposure: = {underpopulation} :extensible: A pattern is said to be extensible if arbitrarily large patterns of the same type can be made by repeating parts of the original pattern in a regular way. :extra extra long: = {long^4} :extra long: = {long^3} :extremely impressive: (p6) Found by Dave Buckingham, August 1976. ....**...... ...*.***.... ...*....*... **.*...**... **.*.....**. ....*****..* ..........** ......*..... .....*.*.... ......*..... :factory: Another word for {gun}, but not used in the case of glider guns. The term is also used for a pattern that repeatedly manufactures objects other than {spaceship}s or {rake}s. In this case the new objects do not move out of the way, and therefore must be used up in some way before the next one is made. The following shows an example of a p144 gun which consists of a p144 block factory whose output is converted into gliders by a p72 oscillator. (This gun is David Bell's improvement of the one Bill Gosper found in July 1994. The p72 oscillator is by Robert Wainwright, 1990, and the block factory is {Achim's p144} minus one of its stabilizing blocks.) .......................**........................** .......................**........................** .........................................**........ ........................................*..*....... .........................................**........ ................................................... ....................................***............ ....................................*.*............ .........**.........................***............ .........**.........................**............. ........*..*.......................***............. ........*..*.**....................*.*............. ........*....**....................***............. ..........**.**.................................... ...............................**.................. .....................**.......*..*................. .....................**........**.................. .................................................** .................................................** ................................................... ....**..................*.......................... **....****..........**..**.***..................... **..**.***..........**....****..................... ....*...................**......................... :familiar fours: Common patterns of four identical objects. The five commonest are {traffic light} (4 blinkers), {honey farm} (4 beehives), {blockade} (4 blocks), {fleet} (4 ships, although really 2 ship-ties) and {bakery} (4 loaves, although really 2 bi-loaves). :fanout: A mechanism that emits two or more objects of some type for each one that it receives. Typically the objects are {glider}s or {Herschel}s; {glider duplicator}s are a special case. :Fast Forward Force Field: The following reaction found by Dieter Leithner in May 1994. In the absence of the incoming LWSS the gliders would simply annihilate one another, but as shown they allow the LWSS to advance 11 spaces in the course of the next 6 generations. A neat illusion. See also {star gate}. (Leithner named the Fast Forward Force Field in honour of his favourite science fiction writer, the physicist Robert L. Forward.) .......*......*.. ........*......** ..**..***.....**. **.**............ ****.........*... .**.........**... ............*.*.. :father: = {parent} :featherweight spaceship: = {glider} :fencepost: Any pattern that stabilizes one end of a {wick}. :Fermat prime calculator: A pattern constructed by Jason Summers in January 2000 that exhibits {infinite growth} if and only if there are no Fermat primes greater than 65537. The question of whether or not it really does exhibit infinite growth is therefore equivalent to a well-known and long-standing unsolved mathematical problem. It will, however, still be growing at generation 10^2585827975. The pattern is based on Dean Hickerson's {primer} and {caber tosser} patterns and a p8 {beehive} {puffer} by Hartmut Holzwart. :F-heptomino: Name given by Conway to the following {heptomino}. **.. .*.. .*.. .*** :figure-8: (p8) Found by Simon Norton in 1970. ***... ***... ***... ...*** ...*** ...*** :filter: Any {oscillator} used to delete some but not all of the {spaceship}s in a stream. An example is the {blocker}, which can be positioned so as to delete every other {glider} in a stream of period 8n+4, and can also do the same for {LWSS} streams. Other examples are the {MW emulator} and {T-nosed p4} (either of which can be used to delete every other LWSS in a stream of period 4n+2), the {fountain} (which does the same for {MWSS} streams) and a number of others, such as the p6 {pipsquirter}, the {pentadecathlon} and the p72 oscillator shown under {factory}. Another example, a p4 oscillator deleting every other HWSS in a stream of period 4n+2, is shown below. (The p4 oscillator here was found, with a slightly larger {stator}, by Dean Hickerson in November 1994.) ..........****............ ....**...******........... ****.**..****.**.......... ******.......**........... .****..................... .......................... ................**........ ..............*....*...... .......................... .............*.*..*.*..... ...........****.**.****... ........*.*....*..*....*.* ........**.**.*....*.**.** ...........*.*......*.*... ........**.*.*......*.*.** ........**.*..........*.** ...........*.*.****.*.*... ...........*.*......*.*... ..........**.*.****.*.**.. ..........*..***..***..*.. ............*..****..*.... ...........**.*....*.**... ...........*..*....*..*... ............*..*..*..*.... .............**....**..... :fire-spitting: (p3) Found by Nicolay Beluchenko, September 2003. ...*...... .***...... *......... .*.***.... .*.....*.. ..*..*.... ..*.*..*.* ........** :fish: A generic term for {LWSS}, {MWSS} and {HWSS}, or, more generally, for any {spaceship}. :fishhook: = {eater1} :fleet: (p1) A common formation of two {ship-tie}s. ....**.... ....*.*... .....**... .......**. **.....*.* *.*.....** .**....... ...**..... ...*.*.... ....**.... :flip-flop: Any p2 {oscillator}. However, the term is also used in two more specific (and non-equivalent) senses: (a) any p2 oscillator whose two {phase}s are mirror images of one another, and (b) any p2 oscillator in which all {rotor} cells die from {underpopulation}. In the latter sense it contrasts with {on-off}. The term has also been used even more specifically for the 12-cell flip-flop shown under {phoenix}. :flip-flops: Another name for the flip-flop shown under {phoenix}. :flipper: Any {oscillator} or {spaceship} that forms its mirror image halfway through its period. :flotilla: A {spaceship} composed of a number of smaller interacting spaceships. Often one or more of these is not a true spaceship and could not survive without the support of the others. The following example shows an {OWSS} escorted by two {HWSS}. ....****....... ...******...... ..**.****...... ...**.......... ............... ...........**.. .*............* *.............. *.............* **************. ............... ............... ....****....... ...******...... ..**.****...... ...**.......... :fly: A certain c/3 {tagalong} found by David Bell, April 1992. Shown here attached to the back of a small spaceship (also by Bell). ..*............................... .*.*.............................. .*.*......................*.*...*. .*.......................**.*.*..* ...........***........*.........*. **.........**..*.**...*..****..... .*.*.........****..*.*..**....**.. .**........*..*...***.....***..... ..*.......*....*..**..**..*..*.... ...*..*...*....*..***.*.*....**... .......*.**....*..****.....*...... ....**...**....*..****.....*...... ....*.*...*....*..***.*.*....**... ...**.....*....*..**..**..*..*.... ....*.*....*..*...***.....***..... .....*.......****..*.*..**....**.. ...........**..*.**...*..****..... ...........***........*.........*. .........................**.*.*..* ..........................*.*...*. :flying machine: = {Schick engine} :fore and back: (p2) Compare {snake pit}. Found by Achim Flammenkamp, July 1994. **.**.. **.*.*. ......* ***.*** *...... .*.*.** ..**.** :forward glider: A {glider} which moves at least partly in the same direction as the {puffer}(s) or {spaceship}(s) under consideration. :fountain: (p4) Found by Dean Hickerson in November 1994, and named by Bill Gosper. See also {filter} and {superfountain}. .........*......... ................... ...**.*.....*.**... ...*.....*.....*... ....**.**.**.**.... ................... ......**...**...... **...............** *..*...*.*.*...*..* .***.*********.***. ....*....*....*.... ...**.........**... ...*...........*... .....*.......*..... ....**.......**.... :fourteener: (p1) ....**. **..*.* *.....* .*****. ...*... :fox: (p2) This is the smallest asymmetric p2 oscillator. Found by Dave Buckingham, July 1977. ....*.. ....*.. ..*..*. **..... ....*.* ..*.*.* ......* :French kiss: (p3) Found by Robert Wainwright, July 1971. *......... ***....... ...*...... ..*..**... ..*....*.. ...**..*.. ......*... .......*** .........* :frog II: (p3) Found by Dave Buckingham, October 1972. ..**...**.. ..*.*.*.*.. ....*.*.... ...*.*.*... ...**.**... .**.....**. *..*.*.*..* .*.*...*.*. **.*...*.** ....***.... ........... ...*.**.... ...**.*.... :frothing puffer: A frothing puffer (or a frothing spaceship) is a {puffer} (or {spaceship}) whose back end appears to be unstable and breaking apart, but which nonetheless survives. The exhaust festers and clings to the back of the puffer/spaceship before breaking off. The first known frothing puffers were c/2, and most were found by slightly modifying the back ends of p2 spaceships. A number of these have periods which are not a multiple of 4 (as with some {line puffer}s). Paul Tooke has also found c/3 frothing puffers. The following p78 c/2 frothing puffer was found by Paul Tooke in April 2001. .......*.................*....... ......***...............***...... .....**....***.....***....**..... ...**.*..***..*...*..***..*.**... ....*.*..*.*...*.*...*.*..*.*.... .**.*.*.*.*....*.*....*.*.*.*.**. .**...*.*....*.....*....*.*...**. .***.*...*....*.*.*....*...*.***. **.........**.*.*.*.**.........** ............*.......*............ .........**.*.......*.**......... ..........*...........*.......... .......**.*...........*.**....... .......**...............**....... .......*.*.*.***.***.*.*.*....... ......**...*...*.*...*...**...... ......*..*...*.*.*.*...*..*...... .........**....*.*....**......... .....**....*...*.*...*....**..... .........*.**.*...*.**.*......... ..........*.*.*.*.*.*.*.......... ............*..*.*..*............ ...........*.*.....*.*........... :frothing spaceship: See {frothing puffer}. :fumarole: (p5) Found by Dean Hickerson in September 1989. In terms of its 7x8 bounding box this is the smallest p5 oscillator. ...**... .*....*. .*....*. .*....*. ..*..*.. *.*..*.* **....** :fuse: A {wick} burning at one end. For examples, see {baker}, {beacon maker}, {blinker ship}, {boat maker}, {cow}, {harvester}, {lightspeed wire}, {pi ship}, {reverse fuse}, {superstring} and {washerwoman}. Useful fuses are usually {clean}. :Gabriel's p138: (p138) The following {oscillator} found by Gabriel Nivasch in October 2002. .......***..... ......*..*..... .......*...*... ..*.....***.... ...*.....*..... **.**.......... *..*.........*. *.*.........*.* .*.........*..* ..........**.** .....*.....*... ....***.....*.. ...*...*....... .....*..*...... .....***....... :galaxy: = {Kok's galaxy} :Game of Life: = {Life} :Game of Life News: A blog reporting on new Life discoveries, started by Heinrich Koenig in December 2004. Dave Greene is also a frequent contributor to the blog, which can be found at {http://gameoflife-news.blogspot.com}. :Garden of Eden: A configuration of ON and OFF cells that can only occur in generation 0. (This term was first used in connection with cellular automata by John W. Tukey, many years before Life.) It was known from the start that there are Gardens of Eden in Life, because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata. Explicit examples have since been constructed, the first by Roger Banks, et al. at MIT in 1971. This example was 9 x 33. In 1974 J. Hardouin-Duparc et al. at the University of Bordeaux 1 produced a 6 x 122 example. The following shows a 12 x 12 example found by Nicolay Beluchenko in February 2006, based on a 13 x 12 one found by Achim Flammenkamp in June 2004. ..*.***..... **.*.*****.* *.*.**.*.*.. .****.*.***. *.*.**.***.* .***.**.*.*. ..*...***..* .*.**.*.*.*. ***.****.*.* **.****...*. .*.*.**..*.. .**.*..**.*. :generation: The fundamental unit of time. The starting pattern is generation 0. :germ: (p3) Found by Dave Buckingham, September 1972. ....**.... .....*.... ...*...... ..*.****.. ..*....*.. .**.*..... ..*.*.**** *.*.*....* **...***.. .......**. :gfind: A program by David Eppstein which uses {de Bruijn graph}s to search for new {spaceship}s. It was with gfind that Eppstein found the {weekender}, and Paul Tooke later used it to find the {dragon}. It is available at {http://www.ics.uci.edu/~eppstein/ca/gfind.c} (C source code only). Compare {lifesrc}. :GIG: A glider injection gate. This is a device for injecting a {glider} into a glider stream. The injected glider is synthesized from one or more incoming {spaceship}s assisted by the presence of the GIG. (This contrasts with some other glider injection reactions which do not require a GIG.) Gliders already in the glider stream pass through the GIG without interfering with it. A GIG usually consists of a small number of oscillators. Glider injection gates are useful for building glider {gun}s with {pseudo}-periods that are of the form nd, where n is a positive integer, and d is a proper divisor of some convenient base gun period (such as 30 or 46), with d > 13. :glasses: (p2) Compare {scrubber} and {spark coil}. ....*........*.... ..***........***.. .*..............*. .*..***....***..*. **.*...*..*...*.** ...*...****...*... ...*...*..*...*... ....***....***.... .................. ....**.*..*.**.... ....*.**..**.*.... :glider: (c/4 diagonally, p4) The smallest, most common and first discovered {spaceship}. This was found by Richard Guy in 1970 while Conway's group was attempting to track the evolution of the {R-pentomino}. The name is due in part to the fact that it is {glide symmetric}. (It is often stated that Conway discovered the glider, but he himself has said it was Guy. See also the cryptic reference ("some guy") in {Winning Ways}.) *** *.. .*. The term "glider" is also occasionally (mis)used to mean "spaceship". :glider-block cycle: An infinite {oscillator} based on the following reaction (a variant of the {rephaser}). The oscillator consists of copies of this reaction displaced 2n spaces from one another (for some n>6) with blocks added between the copies in order to cause the reaction to occur again halfway through the period. The period of the resulting infinite oscillator is 8n-20. (Alternatively, in a cylindrical universe of width 2n the oscillator just consists of two gliders and two blocks.) ...**... ...**... ........ ........ ..*..*.. *.*..*.* .**..**. :glider construction: = {glider synthesis} :glider duplicator: Any reaction in which one input {glider} is converted into two output gliders. This can be done either by {oscillator}s or by {spaceship}s. The most useful glider duplicators are those with low {period}s. The following period 30 glider duplicator demonstrates a simple glider duplicating mechanism found by Dieter Leithner. The input glider stream comes in from the upper left, and the output glider streams leave at the upper and lower right. One of the output glider streams is inverted, so an {inline inverter} is required to complete the duplicator. ..........*.*....................... ...........**....................... ...........*........................ .................................... .................................... .................................... ........................**....*..... ..................*.....**....**.... ...................**........*.*.... ..................**................ .................................... .................................... .................................... .................................... ......................**............ .......................**........... ............*.........*............. ............*.*..................... .............*.*.........**......... **...........*..*.......***......... **...........*.*.....*.**........... ............*.*......*..*........... ............*........*.**........... ........................***.....**.. .........................**.....*.*. ..................................*. ..................................** Spaceship {convoy}s which can duplicate gliders are very useful since they (along with {glider turner}s) provide a means to clean up many dirty puffers by duplicating and turning output gliders so as to impact into the exhaust to clean it up. Glider duplicators (and turners) are known for backward gliders using p2 c/2 spaceships, and for forward gliders using p3 c/3 spaceships. These are the most general duplicators for these speeds. :glider gun: A {gun} which fires {glider}s. :glider injection gate: = {GIG} :gliderless: A {gun} is said to be gliderless if it does not use {glider}s. The purist definition would insist that a glider does not appear anywhere, even incidentally. For a long time the only known way to construct {LWSS}, {MWSS} and {HWSS} guns involved gliders, and it was not until April 1996 that Dieter Leithner constructed the first gliderless gun (a p46 LWSS gun). The following diagram shows the p44 MWSS gun that Dieter Leithner discovered (in a somewhat larger form) in April 1997. This is the smallest known gliderless gun, and also the smallest known MWSS gun. It is based on an important p44 oscillator discovered by Dave Buckingham in early 1992, shown here in an improved form found in January 2005 by Jason Summers using a new p4 {sparker} by Nicolay Beluchenko. Note that a glider shape appears in this gun for three consecutive generations, but always as part of a larger {cluster}, so even a purist would regard this gun as gliderless. .......*.......................................... ..**...*.*....*................................... ..*..**..*.*.**.*..***..**........................ ....**.......**.*.*.**..**........................ ...***.......*.......***.........*................ .......................*.......***................ .......................*......*........***........ ..............................**.......*..*....... .........**..............*.............*.......... .........**.............*..............*...*...... .........................**............*.......... ........................*.*.............*.*....... .................................................. .......................*.*.....***................ ........................*.....*..*..............** **............***.......*......**...........**.*.* **...........*...*..........................**.*.. .............**.**..............................*. .................................**.........**.**. ..............................**.............*.*.. .............................................*.*.. ..............................................*... .............**.**.............*.*................ **...........*...*.............**................. **............***................................. ...........................**..................... ...........................*.*.................... .............................*.................... .............................**................... .................................................. .........**....................................... .........**....................................... .................................................. .......................*.......................... .......................*.......................... ...***.......*.......***.......................... ....**.......**.*.*.**..**........................ ..*..**..*.*.**.*..***..**........................ ..**...*.*....*................................... .......*.......................................... :glider pusher: An arrangement of a {queen bee shuttle} and a {pentadecathlon} that can push the path of a passing glider out by one half-diagonal space. This was found by Dieter Leithner in December 1993 and is shown below. It is useful for constructing complex {gun}s where it may be necessary to produce a number of gliders travelling on close parallel paths. See also {edge shooter}. .........**.............. .........**.............. ......................... ..........*.............. .........*.*............. .........*.*............. ..........*.............. ......................... ......................... .......**.*.**........... .......*.....*........... ........*...*............ .*.......***............. ..*...................... ***...................... ......................... ......................... .................*....*.. ...............**.****.** .................*....*.. :gliders by the dozen: (stabilizes at time 184) In early references this is usually shown in a larger form whose generation 1 is generation 8 of the form shown here. **..* *...* *..** :glider synthesis: Construction of an object by means of {glider} collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement. Glider syntheses for all {still life}s and known {oscillator}s with at most 14 cells were found by Dave Buckingham. Perhaps the most interesting glider syntheses are those of {spaceship}s, because these can be used to create corresponding {gun}s and {rake}s. Many of the c/2 spaceships that are based on {standard spaceship}s have been synthesized, mostly by Mark Niemiec. In June 1998 Stephen Silver found syntheses for some of the {Cordership}s (although it was not until July 1999 that Jason Summers used this to build a Cordership gun). In May 2000, Noam Elkies suggested that a 2c/5 spaceship found by Tim Coe in May 1996 might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March 2003 that Summers and Elkies managed to find a way perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in Life of a rake which fires spaceships that travel in the same direction as the rake but more slowly. A 3-glider synthesis of a {pentadecathlon} is shown in the diagram below. This was found in April 1997 by Heinrich Koenig and came as a surprise, as it was widely assumed that anything using just three gliders would already be known. ......*... ......*.*. ......**.. .......... ***....... ..*....... .*.....**. ........** .......*.. :glider train: A certain {puffer} that produces two rows of {block}s and two backward {glider} waves. Ten of these were used to make the first {breeder}. :glider turner: An reaction in which a {glider} is turned by an {oscillator} or a {spaceship}. In the former case, the glider turner is usually called a {reflector}. Glider turners are easily built using {standard spaceship}s. The following diagram shows a convoy which turns a {forward glider} 90 degrees, with the new glider also moving forwards. .........**......... ........**.****..... .*.......******..... *.........****...... ***................. .................... .................... .................... .................... ...*................ .*...*.............. *................... *....*.............. *****............... .................... .................... .............******. .............*.....* .............*...... ..............*....* ................**.. Small rearrangements of the back two spaceships can alternatively send the output glider into any of the other three directions. See also {glider duplicator} and {reflector}. :glide symmetric: Undergoing simultaneous reflection and translation. A glide symmetric {spaceship} is sometimes called a {flipper}. :gnome: = {fox} :GoE: = {Garden of Eden} :GoL: = {Game of Life} :Golly: A cross-platform open source Life program by Andrew Trevorrow and Tomas Rokicki. Unlike most Life programs it includes the ability to run patterns using the {hashlife} algorithm. It is available from {http://golly.sourceforge.net}. :Gosper glider gun: The first known {gun}, and indeed the first known finite pattern with unbounded growth, found by Bill Gosper in November 1970. It remains by far the smallest known gun. Gosper has since found other guns, see {new gun} and the p144 gun shown under {factory}. ........................*........... ......................*.*........... ............**......**............** ...........*...*....**............** **........*.....*...**.............. **........*...*.**....*.*........... ..........*.....*.......*........... ...........*...*.................... ............**...................... :gourmet: (p32) Found by Dave Buckingham in March 1978. Compare with {pi portraitor} and {popover}. ..........**........ ..........*......... ....**.**.*....**... ..*..*.*.*.....*.... ..**....*........*.. ................**.. .................... ................**.. *.........***..*.*.. ***.......*.*...*... ...*......*.*....*** ..*.*..............* ..**................ .................... ..**................ ..*........*....**.. ....*.....*.*.*..*.. ...**....*.**.**.... .........*.......... ........**.......... :grammar: A set of rules for connecting components together to make an object such as a {spaceship}, {oscillator} or {still life}. :grandfather: = {grandparent} :grandparent: A pattern is said to be a grandparent of the pattern it gives rise to after two generations. See also {parent}. :Gray counter: (p4) Found in 1971. If you look at this in the right way you will see that it cycles through the Gray codes from 0 to 3. Compare with {R2D2}. ......*...... .....*.*..... ....*.*.*.... .*..*...*..*. *.*.*...*.*.* .*..*...*..*. ....*.*.*.... .....*.*..... ......*...... :gray ship: = {grey ship} :great on-off: (p2) ..**.... .*..*... .*.*.... **.*..*. ....**.* .......* ....***. ....*... :grey counter: = {Gray counter} (This form is erroneous, as Gray is surname, not a colour.) :grey ship: A {spaceship} that contains a region with a density of 1/2, and which is {extensible} in such a way that the region of density 1/2 can be made larger than any given square region. See also {with-the-grain grey ship}, {against-the-grain grey ship} and {hybrid grey ship}. :grin: The following common {parent} of the {block}. This name relates to the infamous {Cheshire cat}. See also {pre-block}. *..* .**. :grow-by-one object: A pattern whose population increases by one cell every generation. The smallest known grow-by-one object is the following 44-cell pattern (David Bell's one-cell improvement of a pattern found by Nicolay Beluchenko, September 2005). ........**....... .......**........ .........*....... ...........**.... ..........*...... ................. .........*..**... .**.....**....*.. **.....*.....*... ..*....*.*...**.. ....*..*....**.*. ....**.......**.. ........*....*.** .......*.*..*.**. ........*........ :growing/shrinking line ship: A {line ship} in which the line repeatedly grows and shrinks, resulting in a high-period {spaceship}. :growing spaceship: An object that moves like a {spaceship}, except that its front part moves faster than its back part and a {wick} extends between the two. Put another way, a growing spaceship is a {puffer} whose output is burning {clean}ly at a slower rate than the puffer is producing it. Examples include {blinker ship}s and {pi ship}s. :gull: = {elevener} :gun: Any stationary pattern that emits {spaceship}s (or {rake}s) forever. For examples see {double-barrelled}, {edge shooter}, {factory}, {gliderless}, {Gosper glider gun}, {new gun} and {true}. :gunstar: Any of a series of glider {gun}s of period 144+72n (for all non-negative integers n) constructed by Dave Buckingham in 1990 based on his {transparent block reaction} and Robert Wainwright's p72 oscillator (shown under {factory}). :half bakery: See {bi-loaf}. :half fleet: = {ship-tie} :hammer: To hammer a {LWSS}, {MWSS} or {HWSS} is to smash things into the rear end of it in order to transform it into a different type of {spaceship}. A hammer is the object used to do the hammering. In the following example by Dieter Leithner a LWSS is hammered by two more LWSS to make it into a MWSS. *..*................ ....*...**.......... *...*..***.....****. .****..**.*....*...* ........***....*.... .........*......*..* :hammerhead: A certain front end for c/2 spaceships. The central part of the hammerhead pattern is supported between two {MWSS}. The picture below shows a small example of a {spaceship} with a hammerhead front end (the front 9 columns). ................*.. .**...........*...* **.***.......*..... .*****.......*....* ..*****.....*.****. ......***.*.**..... ......***....*..... ......***.***...... ..........**....... ..........**....... ......***.***...... ......***....*..... ......***.*.**..... ..*****.....*.****. .*****.......*....* **.***.......*..... .**...........*...* ................*.. :handshake: An old MIT name for {lumps of muck}, from the following form (2 generations on from the {stairstep hexomino}): ..**. .*.** **.*. .**.. :harbor: (p5) Found by Dave Buckingham in September 1978. The name is by Dean Hickerson. .....**...**..... .....*.*.*.*..... ......*...*...... ................. .....**...**..... **..*.*...*.*..** *.*.**.....**.*.* .*.............*. ................. .*.............*. *.*.**.....**.*.* **..*.*...*.*..** .....**...**..... ................. ......*...*...... .....*.*.*.*..... .....**...**..... :harvester: (c p4 fuse) Found by David Poyner, this was the first published example of a {fuse}. The name refers to the fact the it produces debris in the form of {block}s which contain the same number of cells as the fuse has burnt up. ................** ...............*.* ..............*... .............*.... ............*..... ...........*...... ..........*....... .........*........ ........*......... .......*.......... ......*........... .....*............ *****............. ****.............. *.**.............. :hashlife: A Life algorithm by Bill Gosper that is designed to take advantage of the considerable amount of repetitive behaviour in many large patterns of interest. This algorithm is described by Gosper in his paper listed in the bibliography at the end of this lexicon. Roughly speaking, the idea is to store subpatterns in a hash table so that the results of their evolution do not need to be recomputed if they arise again at some other place or time in the evolution of the full pattern. This does, however, mean that complex patterns can require substantial amounts of memory. Hashlife provides a means of evolving repetitive patterns millions (or even billions or trillions) of generations further than normal Life algorithms can manage in a reasonable amount of time. It is not, however, suitable for showing a continuous display of the evolution of a pattern, because it works asynchronously - at any given moment it will usually have evolved different parts of the pattern through different numbers of generations. :hassle: See {hassler}. :hassler: An {oscillator} that works by hassling (repeatedly moving or changing) some object. For some examples, see {Jolson}, {baker's dozen}, {toad-flipper}, {toad-sucker} and {traffic circle}. :hat: (p1) Found in 1971. See also {twinhat} and {sesquihat}. ..*.. .*.*. .*.*. **.** :heat: For an {oscillator} or {spaceship}, the average number of cells which change state in each generation. For example, the heat of a {glider} is 4, because 2 cells are born and 2 die every generation. For a period n oscillator with an r-cell {rotor} the heat is at least 2r/n and no more than r(1-(n mod 2)/n). For n=2 and n=3 these bounds are equal. :heavyweight emulator: = {HW emulator} :heavyweight spaceship: = {HWSS} :heavyweight volcano: = {HW volcano} :hebdarole: (p7) Found by Noam Elkies, November 1997. Compare {fumarole}. The smaller version shown below was found soon after by Alan Hensel using a component found by Dave Buckingham in June 1977. The top tens rows can be stabilized by their mirror image (giving an {inductor}) and this was the original form found by Elkies. ...........**........... ....**...*....*...**.... .*..*..*.*....*.*..*..*. *.*.*.**.*....*.**.*.*.* .*..*..*.*.**.*.*..*..*. ....**....*..*....**.... ...........**........... .......*..*..*..*....... ......*.**....**.*...... .......*........*....... ........................ ...**..............**... ...*..****....****..*... ....*.*.*.*..*.*.*.*.... ...**.*...****...*.**... .......**......**....... .........**..**......... .........*..*.*......... ..........**............ :hectic: (p30) Found by Robert Wainwright in September 1984. ......................**............... ......................**............... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... .........*..........**...**............ .......*.*............***.............. ......*.*............*...*............. **...*..*.............*.*.............. **....*.*..............*............... .......*.*......*.*.................... .........*......**..................... .................*...*................. .....................**......*......... ....................*.*......*.*....... ...............*..............*.*....** ..............*.*.............*..*...** .............*...*............*.*...... ..............***............*.*....... ............**...**..........*......... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ...............**...................... ...............**...................... :Heisenburp device: A pattern which can detect the passage of a {glider} without affecting the glider's path or timing. The first such device was constructed by David Bell in December 1992. The term is due to Bill Gosper. The following is an example of the kind of reaction used at the heart of a Heisenburp device. The glider at bottom right alters the reaction of the other two gliders without itself being affected in any way. *.....*.... .**...*.*.. **....**... ........... ........... ........... .........** ........*.* ..........* :helix: A convoy of {standard spaceship}s used in a {Caterpillar} to move some piece of debris at the speed of the Caterpillar. The following diagram illustrates the idea. ...............................*............. .................*............***............ ................***....***....*.**........... .........***....*.**...*..*....***..***...... .........*..*....***...*.......**...*........ .........*.......**....*...*.........*....... .........*...*.........*...*................. ***......*...*.........*..................... *..*.....*..............*.*.................. *.........*.*................................ *............................................ .*.*......................................... ............................................. ............................................. ..........*.................................. .........***................................. .........*.**................................ ..........***................................ ..........**................................. ............................................. ............................................. ...............***........................... ...............*..*....*.....***............. ...............*......***....*..*....*....... ...............*.....**.*....*......***...... ....***.........*.*..***.....*.....**.*...... ....*..*.............***......*.*..***....... ....*................***...........***....... ....*.................**...........***....... .....*.*............................**....... ...........................................*. ..........................................*** .........................................**.* .........................................***. ..........................................**. ............................................. ............................................. ............................................. ............................................. ............................................. ............................................. .........................................*... ..............................***.......***.. ................***.....*....*..*......**.*.. ..........*....*..*....***......*......***... .........***......*....*.**.....*......***... .........*.**.....*.....***..*.*........**... ..........***..*.*......***.................. .*........***...........***.................. ***.......***...........**................... *.**......**................................. .***......................................*.. .**......................................***. ........................................**.*. ........................................***.. .........................................**.. .........***................................. ........*..*................................. ...........*................................. ...........*................................. ........*.*.................................. :heptaplet: Any 7-cell {polyplet}. :heptapole: (p2) The {barberpole} of length 7. **........ *.*....... .......... ..*.*..... .......... ....*.*... .......... ......*.*. .........* ........** :heptomino: Any 7-cell {polyomino}. There are 108 such objects. Those with names in common use are the {B-heptomino}, the {Herschel} and the {pi-heptomino}. :Herschel: (stabilizes at time 128) The following pattern which occurs at generation 20 of the {B-heptomino}. *.. *** *.* ..* :Herschel conduit: A {conduit} that moves a {Herschel} from one place to another. See also {Herschel loop}. Sixteen simple {stable} Herschel conduits are currently known, having been discovered from 1995 onwards by Dave Buckingham (DJB) and Paul Callahan (PBC). (Of course, the number depends on what is meant by "simple".) These are shown in the following table. In this table "steps" is the number of {step}s, "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, f = flipped), and "dx" and "dy" give the displacement of the centre cell of the Herschel (assumed to start in the orientation shown above). ------------------------------------ steps m dx dy discovery ------------------------------------ 64 R -11 9 DJB, Sep 1995 77 Ff -25 -8 DJB, Aug 1996 112 L -12 -33 DJB, Jul 1996 116 F -32 1 PBC, Feb 1997 117 F -40 -6 DJB, Jul 1996 119 Ff -20 14 DJB, Sep 1996 125 Bf 9 -17 PBC, Nov 1998 153 Ff -48 -4 PBC, Feb 1997 156 L -17 -41 DJB, Aug 1996 158 Ff -27 -5 DJB, Jul 1996 166 F -49 3 PBC, May 1997 176 Ff -45 0 PBC, Oct 1997 190 R -24 16 DJB, Jul 1996 200 Lf -17 -40 PBC, Jun 1997 202 Rf -7 32 DJB, May 1997 222 Bf 6 -16 PBC, Oct 1998 ------------------------------------ See also {Herschel transceiver}. :Herschel loop: A cyclic {Herschel track}. Although no loop of length less than 256 generations has been constructed it is possible to make {oscillator}s of smaller periods by putting more than one Herschel in the track. In this way oscillators, and in most cases {gun}s, of all periods from 54 onwards can now be constructed (although the p55 case is a bit strange, shooting itself with gliders in order to stabilize itself). See also {emu} and {omniperiodic}. :Herschel receiver: A pattern found by Paul Callahan in 1996, as part of the first stable glider {reflector}. Used as a receiver, it converts two parallel input gliders (with path separations of 2, 5, or 6) to an {R-pentomino}, which is then converted to a Herschel by one of two known mechanisms (the first of which was found by Dave Buckingham way back in 1972, and the second by Stephen Silver in October 1997). The version using Buckingham's R-to-Herschel converter is shown below. ...............................................*.* ......................................**.......**. ......................................**........*. ...**............................................. ...*.............................................. ....*............................................. ...**............................................. ............**.................................... ...........*.*.................................... ............*..............................*...... ......................................**...*.*.... .....................................*..*..**..... **....................................**.......... **.............................**................. ...............................**................. .................................................. .................................................. .................................................. .................................................. .................................................. .................................................. ............................................**.... ............................................**.... ........................................**........ ........................................*.*....... ..........................................*....... ..........................................**...... .............................**................... .............................**................... .................................................. .................................................. ...........................**..................... ...........................**..................... :Herschel track: A {track} for {Herschel}s. See also {B track}. :Herschel transceiver: An adjustable {Herschel conduit} made up of a {Herschel transmitter} and a {Herschel receiver}. The intermediate stage consists of two {glider}s on parallel tracks, so the transmitter and receiver can be separated by any required distance. The conduit may be {stable}, or may contain low-period {oscillator}s. :Herschel transmitter: Any {Herschel}-to-{glider} {converter} that produces two gliders on parallel tracks which can be used as input to a {Herschel receiver}. If the gliders are far enough apart, a suitably oriented mirror image of the receiver will also work: the first glider triggers the receiver and the second glider deletes the extra beehive. The following diagram shows a {stable} Herschel transmitter found by Paul Callahan in May 1997: ......**........... .....*.*........... ...***............. ..*...*......*..... ..**.**......***... .............*.*... ...............*... ................... ................... **.*............... *.**............... ................... ................... ................... ...............**.. ...............*... ................*** ..................* Examples of small reversible p6 and p7 transmitters are also known. :Hertz oscillator: (p8) Compare {negentropy}, and also {cauldron}. Found by Conway's group in 1970. ...**.*.... ...*.**.... ........... ....***.... ...*.*.*.** ...*...*.** **.*...*... **.*...*... ....***.... ........... ....**.*... ....*.**... :hexadecimal: = {beehive and dock} :hexaplet: Any 6-cell {polyplet}. :hexapole: (p2) The {barberpole} of length 6. **....... *.*...... ......... ..*.*.... ......... ....*.*.. ......... ......*.* .......** :hexomino: Any 6-cell {polyomino}. There are 35 such objects. For some examples see {century}, {stairstep hexomino}, {table}, {toad} and {Z-hexomino}. :H-heptomino: Name given by Conway to the following {heptomino}. After one generation this is the same as the {I-heptomino}. **.. .*.. .*** ..*. :hive: = {beehive} :hivenudger: (c/2 orthogonally, p4) A {spaceship} found by Hartmut Holzwart in July 1992. (The name is due to Bill Gosper.) It consists of a {pre-beehive} escorted by four {LWSS}. In fact any LWSS can be replaced by a {MWSS} or a {HWSS}, so that there are 45 different single-hive hivenudgers. ****.....*..* *...*...*.... *.......*...* .*..*...****. ............. .....**...... .....**...... .....**...... ............. .*..*...****. *.......*...* *...*...*.... ****.....*..* Wider versions can be made by stabilizing the front of the extended "pre-beehive", as in the {line puffer} shown below. .........*.*.................. ........*..*.................. .......**..................... ......*...*................... .....***.*.................... ..**.......................... .*...*****.......****.....*..* *...*............*...*...*.... *.....**.........*.......*...* ***...****........*..*...****. .*.......*.................... .**...................**...... .*.*..................**...... .**..**.*........*.*..**...... ..*.***.*...*.****.*..**...... .........**.*.**..*...**...*** ....******.**...****..**...*** .....*....***......*..**...*** ......**.....**..**...**...... .......*..*.....****..**...... ........*.*.**.....*..**...... ......................**...... .............................. ..................*..*...****. .................*.......*...* .................*...*...*.... .................****.....*..* :honeycomb: (p1) ..**.. .*..*. *.**.* .*..*. ..**.. :honey farm: (p1) A common formation of four beehives. ......*...... .....*.*..... .....*.*..... ......*...... ............. .**.......**. *..*.....*..* .**.......**. ............. ......*...... .....*.*..... .....*.*..... ......*...... :hook: Another term for a {bookend}. It is also used for other hook-shaped things, such as occur in the {eater1} and the {hook with tail}, for example. :hook with tail: (p1) For a long time this was the smallest {still life} without a well-established name. It is now a vital component of the smallest known {HWSS} {gun}, where it acts as a {rock}. *.*.. **.*. ...*. ...** :houndstooth agar: The p2 {agar} that results from tiling the plane with the following pattern. .*** .*.. ..*. ***. :house: The following {induction coil}. It is generation 3 of the {pi-heptomino}. See {spark coil} and {dead spark coil}. .***. *...* **.** :hustler: (p3) Found by Robert Wainwright, June 1971. .....**.... .....**.... ........... ...****.... *.*....*... **.*...*... ...*...*.** ...*....*.* ....****... ........... ....**..... ....**..... :hustler II: (p4) ....*........... ....***......... .......*........ ......*..**..... *.**.*.**..*.... **.*.*.....*.... .....*....*..... ....*.....*.*.** ....*..**.*.**.* .....**..*...... ........*....... .........***.... ...........*.... :HW emulator: (p4) Found by Robert Wainwright in June 1980. See also {emulator}. .......**....... ..**.*....*.**.. ..*..........*.. ...**......**... ***..******..*** *..*........*..* .**..........**. :HWSS: (c/2 orthogonally, p4) A heavyweight spaceship, the fourth most common {spaceship}. Found by Conway in 1970. See also {LWSS} and {MWSS}. ...**.. .*....* *...... *.....* ******. :HWSS emulator: = {HW emulator} :HW volcano: (p5) A p5 {domino} {sparker}, found by Dean Hickerson in February 1995. There are at least two known forms for this, one of which is shown below. .........*.......................... ........*.*......................... ......***.*......................... .....*....**.*...................... .....*.**...**......**.............. ....**.*.**.........*.*............. .........*.*****......*..*.**....... ..*.**.**.*.....*....**.*.**.*...... .....**.....****........*....*...... *...*.*..*...*.*....**.*.****.**.... *...*.*..**.*.**.**....*.*....*.*... .....**...***.**.*.***.*..***...*... ..*.**.**.**.............*.*..*.*.** ...........*......*.*.*.*..**.*.*.*. ....**.*.*.**......**.*.*.*...*.*.*. .....*.**.*..*.......*.**..****.**.. .....*....*.*........*...**......... ....**....**........**...*..*....... ...........................**....... :hybrid grey ship: A {grey ship} containing more than one type of region of density 1/2, usually a combination of a {with-the-grain grey ship} and an {against-the-grain grey ship}. :I-heptomino: Name given by Conway to the following {heptomino}. After one generation this is the same as the {H-heptomino}. **.. .*.. .**. ..** :IMG: = {intermitting glider gun} :Immigration: A form of {colorized Life} in which there are two types of ON cell, a newly-born cell taking the type of the majority of its three {parent cells} and surviving cells remaining of the same type as in the previous generation. :induction coil: Any object used to stabilize an edge (or edges) without touching. The tubs used in the {Gray counter} are examples, as are the blocks and snakes used in the {Hertz oscillator} and the heptomino at the bottom of the {mathematician}. :inductor: Any {oscillator} with a row of dead cells down the middle and whose two halves are mirror images of one another, both halves being required for the oscillator to work. The classic examples are the {pulsar} and the {tumbler}. If still lifes are considered as p1 oscillators then there are numerous simple examples such as {table on table}, {dead spark coil} and {cis-mirrored R-bee}. Some spaceships, such as the {brain}, the {snail} and the {spider} use the same principle. :infinite glider hotel: A pattern by David Bell, named after Hilbert's "infinite hotel" scenario in which a hotel with an infinite number of rooms has room for more guests even if it is already full, simply by shuffling the old guests around. In this pattern, two pairs of {Cordership}s moving at c/12 are pulling apart such that there is an ever-lengthening {glider} track between them. Every 128 generations another glider is injected into the glider track, joining the gliders already circulating there. The number of gliders in the track therefore increases without limit. The tricky part of this construction is that even though all the previously injected gliders are repeatedly flying through the injection point, that point is guaranteed to be empty when it is time for the next glider to be injected. :infinite growth: Growth of a finite pattern such that the {population} tends to infinity, or at least is unbounded. Sometimes the term is used for growth of something other than population (for example, length), but here we will only consider infinite population growth. The first known pattern with infinite growth in this sense was the {Gosper glider gun}. An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a {switch engine} could be stabilized by a {pre-block} in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single {cluster}. This produces a stabilized switch engine of the block-laying type. ......*. ....*.** ....*.*. ....*... ..*..... *.*..... Nick Gotts and Paul Callahan have also shown that there is no infinite growth pattern with fewer than 10 cells, so that the question has now been answered. Also of interest is the following pattern (again found by Callahan), which is the only 5x5 pattern with infinite growth. This too emits a block-laying switch engine. ***.* *.... ...** .**.* *.*.* Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470x1 in the first version, reduced to 5447x1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39x1 pattern shown below. This produces two block-laying switch engines, stability being achieved at generation 1483. ********.*****...***......*******.***** Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see {breeder}) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as {sawtooth}s and a {caber tosser}. See also {Fermat prime calculator}. :initials: = {monogram} :inline inverter: The following reaction in which a p30 {gun} can be used to invert the presence or absence of gliders in a p30 stream, with the output glider stream being in the same direction as the input glider stream. ................*................... .................*.................. ...............***.................. .................................... .......................*.*.......... .....................*...*.......... .............*.......*.............. ............****....*....*........** ...........**.*.*....*............** **........***.*..*...*...*.......... **.........**.*.*......*.*.......... ............****.................... .............*...................... :integral: = {integral sign} :integral sign: (p1) ...** ..*.* ..*.. *.*.. **... :intentionless: = {elevener} :interchange: (p2) A common formation of six blinkers. ..***....***.. .............. *............* *............* *............* .............. ..***....***.. :intermitting glider gun: Despite the name, an intermitting glider gun (IMG) is more often an {oscillator} than a {gun}. There are two basic types. A type 1 IMG consists of two guns firing at one another in such a way that each gun is temporarily disabled on being hit by a glider from the other gun. A type 2 IMG consists of a single gun firing at a 180-degree glider {reflector} in such a way that returning gliders temporarily disable the gun. Both types of IMG can be used to make glider guns of periods that are multiples of the base period. This is done by firing another gun across the two-way intermittent glider stream of the IMG in such a way that gliders only occasionally escape. :island: The individual {polyplet}s of which a {stable} pattern consists are sometimes called islands. So, for example, a {boat} has only one island, while an {aircraft carrier} has two, a {honey farm} has four and the standard form of the {eater3} has five. :Iwona: (stabilizes at time 28786) The following {methuselah} found by Andrzej Okrasinski in August 2004. ..............***... .................... .................... .................... .................... .................... ..*................. ...**............... ...*..............*. ..................*. ..................*. ...................* ..................** .......**........... ........*........... .................... .................... .................... .................... **.................. .*.................. :J: = {Herschel} :jack: (p4) Found by Robert Wainwright, April 1984. ...*.....*... ...**...**... *..**...**..* ***..*.*..*** .....*.*..... ***..*.*..*** *..**...**..* ...**...**... ...*.....*... :jagged lines: A pattern constructed by Dean Hickerson in May 2005 that uses {puffer}s to produce a line of {bi-block}s that weaves back and forth in a complicated way. :jam: (p3) Found by Achim Flammenkamp in 1988, but not widely known about until its independent discovery (and naming) by Dean Hickerson in September 1989. Compare with {mold}. In fact this is really very like {caterer}. In terms of its 7x7 {bounding box} it ties with {trice tongs} as the smallest p3 {oscillator}. ...**. ..*..* *..*.* *...*. *..... ...*.. .**... :Jaws: A {breeder} constructed by Nick Gotts in February 1997. In the original version Jaws had an initial {population} of 150, which at the time was the smallest for any known pattern with superlinear growth. In November 1997 Gotts produced a 130-cell Jaws using some {switch engine} {predecessor}s found by Paul Callahan. Jaws has since been beaten by the even smaller {mosquito}es, {teeth}, {catacryst} and {metacatacryst}. Jaws consists of eight pairs of switch engines which produce a new block-laying switch engine (plus masses of junk) every 10752 generations. It is therefore an MMS breeder. :JC: = {dead spark coil} :JHC: John Horton Conway. Also another name for {monogram}. :J-heptomino: = {Herschel} :Jolson: (p15) Two {block}s {hassle}d by two {pentadecathlon}s. Found by Robert Wainwright in November 1984 and named by Bill Gosper. A p9 version using {snacker}s instead of pentadecathlons is also possible. .**......**.. *..*....*..*. *..*....*..*. *..*....*..*. .**......**.. ............. ............. .......*..... .....*..*.**. ......**..**. ............. ............. ......****... .....******.. ....********. ...**......** ....********. .....******.. ......****... :Justyna: (stabilizes at time 26458) The following {methuselah} found by Andrzej Okrasinski in May 2004. .................*.... ................*..*.. .................***.. .................*..*. ...................... **................*... .*................*... ..................*... ...................... ...................... ...................... ...................... ...................... ...................... ...................... ...................*** ...........***........ :keys: See {short keys}, {bent keys} and {odd keys}. :kickback reaction: The following collision of two {glider}s whose product is a single glider travelling in the opposite direction to one of the original gliders. This is important in the proof of the existence of a {universal constructor}, and in Bill Gosper's {total aperiodic}, as well as a number of other constructions. .....*.. ......** .**..**. *.*..... ..*..... :kidney: A Gosperism for {century}. See also {diuresis}. :killer toads: A pair of {toad}s acting together so that they can eat things. Here, for example, are some killer toads eating a {HWSS}. Similarly they can eat a {MWSS} (but not a {LWSS}). For another example see {twirling T-tetsons II}. See also {candlefrobra}. ..**.......*** *....*....***. ......*....... *.....*....... .******....... ..........***. ...........*** :Klein bottle: As an alternative to a {torus}, it's possible to make a finite Life universe in the form of a Klein bottle. The simplest way to do this is to use an m x n rectangle with the top edge joined to the bottom edge (as for a torus) and the left edge twisted and joined to the right. :knightship: Any {spaceship} of type (2m,m)/n. Such spaceships do exist (see {universal constructor}), but no concrete example is known. A knightship must be asymmetric and its period must be at least 6, which makes searching for them using programs like {lifesrc} very difficult. By analogy with the corresponding fairy chess pieces, spaceships of types (3m,m)/n, (3m,2m)/n and (4m,m)/n would presumably be called camelships, zebraships and giraffeships, respectively. But no examples of these are known either, and they are even more difficult to search for. :Kok's galaxy: (p8) Found by Jan Kok in 1971. See {converter} for a use of this {sparker}. ******.** ******.** .......** **.....** **.....** **.....** **....... **.****** **.****** :lake: Any still life consisting of a simple closed curve made from diagonally connected {domino}es. The smallest example is the {pond}, and the next smallest is this (to which the term is sometimes restricted): ....**.... ...*..*... ...*..*... .**....**. *........* *........* .**....**. ...*..*... ...*..*... ....**.... :Laputa: (p2) Found by Rich Schroeppel, September 1992. ...**.**.... ...**.*...** ........*..* .******.***. *..*.*...... **...*.**... ....**.**... :large S: = {big S} :Lidka: (stabilizes at time 29053) A {methuselah} found by Andrzej Okrasinski in July 2005. ..........***.. ..........*.... ..........*...* ...........*..* ............*** ............... .*............. *.*............ .*............. The following variant, pointed out by David Bell, has two fewer cells and lasts two generations longer. ..........***.. ............... ...........**.* ............*.* ..............* ............... .*............. *.*............ .*............. :Life: A 2-dimensional 2-state {cellular automaton} discovered by John Conway in 1970. The states are referred to as ON and OFF (or live and dead). The transition rule is as follows: a cell that is ON will remain ON in the next generation if and only if exactly 2 or 3 of the 8 adjacent cells are also ON, and a cell that is OFF will turn ON if and only if exactly 3 of the 8 adjacent cells are ON. (This is more succinctly stated as: "If 2 of your 8 nearest neighbours are ON, don't change. If 3 are ON, turn ON. Otherwise, turn OFF.") :Life32: A freeware Life program by Johan Bontes for Microsoft Windows 95/98/ME/NT/2000/XP: {http://www.xs4all.nl/~jbontes/}. :LifeLab: A shareware Life program by Andrew Trevorrow for the Macintosh (MacOS 8.6 or later): {http://www.trevorrow.com/lifelab/}. :LifeLine: A newsletter edited by Robert Wainwright from 1971 to 1973. During this period it was the main forum for discussions about Life. The newsletter was nominally quarterly, but the actual dates of its eleven issues were as follows: Mar, Jun, Sep, Dec 1971 Sep, Oct, Nov, Dec 1972 Mar, Jun, Sep 1973 :Lifenthusiast: A Life enthusiast. Term coined by Robert Wainwright. :lifesrc: David Bell's Life search program, for finding new {spaceship}s and {oscillator}s. This is a C implementation of an algorithm developed by Dean Hickerson in 6502 assembler. Most of the spaceships and many of the oscillators shown in this lexicon were found with lifesrc or by Hickerson's original program. Although lifesrc itself is a command-line program, Jason Summers has made a GUI version called {WinLifeSearch} for Microsoft Windows. The lifesrc algorithm is only useful for very small periods, as the amount of computing power required rises rapidly with increasing period. For most purposes, period 7 is the practical limit with current hardware. Lifesrc is available from {http://www.canb.auug.org.au/~dbell/} (source code only). Compare {gfind}. :light bulb: (p2) Found in 1971. .**.*.. .*.**.. ....... ..***.. .*...*. .*...*. ..*.*.. *.*.*.* **...** The same {rotor} can be embedded in a slightly smaller {stator} like this: ...*..... .***..... *........ ******... ......*.. ..*...*.. ..**.*... ......*** ........* :lightspeed ribbon: = {superstring} :lightspeed wire: Any {wick} that can burn non-destructively at the speed of light. These are potentially useful for various things, but so far no one has found the necessary mechanisms. The following diagram shows an example of a lightspeed wire, with a small defect that travels along it at the speed of light. ....**..**..**..**..**..**..**..**..**..**..**..**..**.... ....**..**..**..**..**..**..**..**..**..**..**..**..**.... .......................................................... ..******************************************************.. .*......*...............................................*. *.*****....*********************************************.* .*.....*................................................*. ..******************************************************.. .......................................................... ....**..**..**..**..**..**..**..**..**..**..**..**..**.... ....**..**..**..**..**..**..**..**..**..**..**..**..**.... :lightweight emulator: = {LW emulator} :lightweight spaceship: = {LWSS} :lightweight volcano: = {toaster} :line puffer: A {puffer} which produces its output by means of an orthogonal line of cells at right angles to the direction of travel. The archetypal line puffer was found by Alan Hensel in March 1994, based on a {spaceship} found earlier that month by Hartmut Holzwart. The following month Holzwart found a way to make {extensible} c/2 line puffers, and Hensel found a much smaller stabilization the following day. But in October 1995 Tim Coe discovered that for large widths these were often unstable, although typically lasting millions of generations. In May 1996, however, Coe found a way to fix the instability. The resulting puffers appear to be completely stable and to exhibit an exponential increase in period as a function of width, although neither of these things has been proved. Line puffers have enabled the construction of various difficult periods for c/2 spaceships and puffers, including occasionally periods which are not multiples of 4 and which would therefore be impossible to attain with the usual type of construction based on {standard spaceship}s. (See {frothing puffer} for another method of constructing such periods.) In particular, the first c/2 {rake} with period not divisible by 4 was achieved in January 2000 when David Bell constructed a p42 {backrake} by means of line puffers. See also {hivenudger} and {puff suppressor}. :line ship: A {spaceship} in which the front end is a {linestretcher}, the line being eaten by the back end. :linestretcher: A {wickstretcher} that stretches a single diagonal line of cells. The first example was constructed by Jason Summers in March 1999; this was c/12 and used {switch engine} based puffers found earlier by Dean Hickerson. The first c/4 example was found by Hartmut Holzwart in November 2004. :loading dock: (p3) Found by Dave Buckingham, September 1972. ....*.... ..***.... .*...**.. *.**...*. .*...**.* ..**...*. ....***.. ....*.... :loaf: (p1) .**. *..* .*.* ..*. :loaflipflop: (p15) Here four {pentadecathlon}s {hassle} a {loaf}. Found by Robert Wainwright in 1990. ................*................. ...............***................ .................................. .................................. ...............***................ .................................. ...............*.*................ ...............*.*................ .................................. ...............***................ .................................. .................................. ...............***................ ................*................. .................................. .*..*.**.*..*...............**.... **..*....*..**...**.......*....*.. .*..*.**.*..*...*..*.....*......*. ................*.*.....*........* .................*......*........* ........................*........* .........................*......*. ..........................*....*.. ............................**.... ..................***............. .................*...*............ ................*.....*........... .................................. ...............*.......*.......... ...............*.......*.......... .................................. ................*.....*........... .................*...*............ ..................***............. :loaf on loaf: = {bi-loaf} :loaf siamese barge: (p1) ..**. .*..* *.*.* .*.*. ..*.. :LoM: = {lumps of muck} :lone dot agar: An {agar} in which every live cell is isolated in every generation. :lonely bee: = {worker bee} :long: A term applied to an object that is of the same basic form as some standard object, but longer. For examples see {long barge}, {long boat}, {long bookend}, {long canoe}, {long shillelagh}, {long ship} and {long snake}. :long^3: The next degree of longness after {long long}. Some people prefer "extra long". :long^4: The next degree of longness after {long^3}. Some people prefer "extra extra long". :long barge: (p1) .*... *.*.. .*.*. ..*.* ...*. :long boat: (p1) .*.. *.*. .*.* ..** :long bookend: The following {induction coil}, longer than a {bookend}. ...** *...* ****. :long canoe: (p1) ....** .....* ....*. ...*.. *.*... **.... :long hat: = {loop} :long hook: = {long bookend} :long house: = {dock} :long integral: (p1) ..** .*.* .*.. ..*. *.*. **.. :long long: The next degree of longness after {long}. Some people prefer "very long". :long long barge: (p1) .*.... *.*... .*.*.. ..*.*. ...*.* ....*. :long long boat: (p1) .*... *.*.. .*.*. ..*.* ...** :long long canoe: (p1) .....** ......* .....*. ....*.. ...*... *.*.... **..... :long long ship: (p1) **... *.*.. .*.*. ..*.* ...** :long long snake: (p1) **.... *.*... ...*.* ....** :long shillelagh: (p1) **..** *..*.* .**... :long ship: (p1) **.. *.*. .*.* ..** :long sinking ship: = {long canoe} :long snake: (p1) **... *.*.* ...** :loop: (p1) .**.. *..*. .*.*. **.** :low-density Life: = {sparse Life} :lumps of muck: The common evolutionary sequence that ends in the {blockade}. The name is sometimes used of the blockade itself, and can in general be used of any stage of the evolution of the {stairstep hexomino}. :LW emulator: (p4) The smallest (and least useful) {emulator}, found by Robert Wainwright in June 1980. ..**.*..*.**.. ..*........*.. ...**....**... ***..****..*** *..*......*..* .**........**. :LWSS: (c/2 orthogonally, p4) A lightweight spaceship, the smallest known orthogonally moving {spaceship}, and the second most common (after the {glider}). Found by Conway in 1970. See also {MWSS} and {HWSS}. .*..* *.... *...* **** :LWSS emulator: = {LW emulator} :LWTDS: Life Worker Time Deficiency Syndrome. Term coined by Dieter Leithner to describe the problem of having to divide scarce time between Life and real life. :LW volcano: = {toaster} :mango: (p1) .**.. *..*. .*..* ..**. :mathematician: (p5) Found by Dave Buckingham, 1972. ....*.... ...*.*... ...*.*... ..**.**.. *.......* ***...*** ......... ********* *.......* ...****.. ...*..**. :Max: A name for the smallest known {spacefiller}. The name represents the fact that the growth rate is the fastest possible. (This has not quite been proved, however. There remains the possibility, albeit not very likely, that a periodic {agar} could have an average {density} greater than 1/2, and a spacefiller stretching such an agar at the same speed as the known spacefillers would have a faster average growth rate.) :mazing: (p4) In terms of its minimum {population} of 12 this ties with {mold} as the smallest p4 {oscillator}. Found by Dave Buckingham in December 1973. For some constructions using mazings, see {popover} and {sixty-nine}. ...**.. .*.*... *.....* .*...** ....... ...*.*. ....*.. :medium fish: = {MWSS} :metacatacryst: A 52-cell pattern exhibiting quadratic growth. Found by Nick Gotts, December 2000. This is currently the smallest known pattern (in terms of initial population) with superlinear growth. See also {catacryst}. :metamorphosis: An {oscillator} built by Robert Wainwright that uses the following reaction (found by Bill Gosper) to turn {glider}s into {LWSS}, and converts these LWSS back into gliders by colliding them head on. (There are in fact two ways to do the following reaction, because the {spark} of the {twin bees shuttle} is symmetric.) ...................*......... ....................*........ ..................***........ ............................. ............................. ............................. ............................. ............................. ............*...*.....*.**... **.........*.....*....*.*.*.. **.........*.........*....*.. ...........**...*.....*.*.*.. .............***......*.**... ............................. .............***............. ...........**...*............ **.........*...............** **.........*.....*.........** ............*...*............ :metamorphosis II: An oscillator built by Robert Wainwright in December 1994 based on the following p30 {glider}-to-{LWSS} {converter}. This converter was first found by Paul Rendell, January 1986 or earlier, but wasn't widely known about until Paul Callahan rediscovered it in December 1994. ......................*. .....................*.. .....................*** ........................ ........................ .........*.*............ .........*..*........... **..........**.......... **........*...**........ .....**.....**.......... ....*....*..*........... .........*.*............ ........................ ........................ ........................ ........................ ................*....... ...............***...... ..............*****..... .............*.*.*.*.... .............**...**.... ........................ ........................ ................*....... ...............*.*...... ...............*.*...... ................*....... ...............**....... ...............**....... ...............**....... :methuselah: Any small pattern that stabilizes only after a long time. Term coined by Conway. Examples include {rabbits}, {acorn}, the {R-pentomino}, {blom}, {Iwona}, {Justyna} and {Lidka}. See also {ark}. :Mickey Mouse: (p1) A name proposed by Mark Niemiec for the following {still life}: .**....**. *..*..*..* *..****..* .**....**. ...****... ...*..*... ....**.... :middleweight emulator: = {MW emulator} :middleweight spaceship: = {MWSS} :middleweight volcano: = {MW volcano} :mini pressure cooker: (p3) Found by Robert Wainwright before June 1972. Compare {pressure cooker}. .....*..... ....*.*.... ....*.*.... ...**.**... *.*.....*.* **.*.*.*.** ...*...*... ...*.*.*... ....*.*.... .....*..... :M.I.P. value: The maximum {population} divided by the initial population for an unstable pattern. For example, the {R-pentomino} has an M.I.P. value of 63.8, since its maximum population is 319. The term is no longer in use. :MIT oscillator: = {cuphook} :MMM breeder: See {breeder}. :MMS breeder: See {breeder}. :mod: The smallest number of generations it takes for an {oscillator} or {spaceship} to reappear in its original form, possibly subject to some rotation or reflection. The mod may be equal to the {period}, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators which rotate 180 degrees every half period, and also for {flipper}s). :mold: (p4) Found by Achim Flammenkamp in 1988, but not widely known until Dean Hickerson rediscovered it (and named it) in August 1989. Compare with {jam}. In terms of its minimum {population} of 12 it ties with {mazing} as the smallest p4 {oscillator}. But in terms of its 6x6 {bounding box} it wins outright. In fact, of all oscillators that fit in a 6x7 box it is the only one with {period} greater than 2. ...**. ..*..* *..*.* ....*. *.**.. .*.... :monogram: (p4) Found by Dean Hickerson, August 1989. **...** .*.*.*. .**.**. .*.*.*. **...** :moose antlers: (p1) **.....** *.......* .***.***. ...*.*... ....*.... :mosquito: See {mosquito1}, {mosquito2}. {mosquito3}, {mosquito4} and {mosquito5}. :mosquito1: A {breeder} constructed by Nick Gotts in September 1998. The original version had an initial population of 103, which was then the smallest for any known pattern with superlinear growth (beating the record previously held by {Jaws}). This was reduced to 97 by Stephen Silver the following month, but was then almost immediately superseded by {mosquito2}. Mosquito1 consists of the classic {puffer train} plus four {LWSS} and four {MWSS} (mostly in {predecessor} form, to keep the population down). Once it gets going it produces a new block-laying {switch engine} (plus a lot of junk) every 280 generations. It is therefore an MMS breeder, albeit a messy one. :mosquito2: A {breeder} constructed by Nick Gotts in October 1998. Its initial population of 85 was for a couple of hours the smallest for any known pattern with superlinear growth, but was then beaten by {mosquito3}. Mosquito2 is very like {mosquito1}, but uses two fewer {MWSS} and one more {LWSS}. :mosquito3: A {breeder} constructed by Nick Gotts in October 1998. Its initial population of 75 was at the time the smallest for any known pattern with superlinear growth, but was beaten a few days later by {mosquito4}. Mosquito3 has one less {LWSS} than {mosquito2}. It is somewhat different from the earlier mosquitoes in that the {switch engine}s it makes are glider-producing rather than block-laying. :mosquito4: A slightly improved version of {mosquito3} which Stephen Silver produced in October 1998 making use of another discovery of Nick Gotts (September 1997): an 8-cell pattern that evolves into a {LWSS} plus some junk. Mosquito4 is a {breeder} with an initial population of 73, at the time the smallest for any known pattern with superlinear growth, but superseded a few days later by {mosquito5}. :mosquito5: A slightly improved version of {mosquito4} which Nick Gotts produced in October 1998. The improvement is of a similar nature to the improvement of mosquito4 over mosquito3. Mosquito5 is a {breeder} with an initial population of 71. At the time, this was the smallest population for any known pattern with superlinear growth, but it has since been superseded by {teeth}, {catacryst} and {metacatacryst}. :mould: = {mold} :moving sawtooth: A {sawtooth} such that no cell is ON for more than a finite number generations. David Bell has constructed patterns of this type, with a c/2 front end and a c/3 back end. :MSM breeder: See {breeder}. :multi-state Life: = {colorized Life} :multum in parvo: (stabilizes at time 3933) A {methuselah} found by Charles Corderman, but not as long-lasting as his {acorn}. ...*** ..*..* .*.... *..... :muttering moat: Any {oscillator} whose {rotor} consists of a closed chain of cells each of which is adjacent to exactly two other rotor cells. Compare {babbling brook}. Examples include the {bipole}, the {blinker}, the {clock}, the {cuphook}, the {Gray counter}, the {quad}, the {scrubber}, the {skewed quad} and the p2 {snake pit}. The following diagram shows a p2 example (by Dean Hickerson, May 1993) with a larger rotor. See {ring of fire} for a very large one. **..... *.*.**. .....*. .*..*.. ..*.... ..*.*.* .....** :MW emulator: (p4) Found by Robert Wainwright in June 1980. See also {emulator} and {filter}. .......*....... ..**.*...*.**.. ..*.........*.. ...**.....**... ***..*****..*** *..*.......*..* .**.........**. :MWSS: (c/2 orthogonally, p4) A middleweight spaceship, the third most common {spaceship}. Found by Conway in 1970. See also {LWSS} and {HWSS}. ...*.. .*...* *..... *....* *****. :MWSS emulator: = {MW emulator} :MWSS out of the blue: The following reaction, found by Peter Rott in November 1997, in which a {LWSS} passing by a p46 {oscillator} creates a {MWSS} travelling in the opposite direction. Together with some reactions found by Dieter Leithner, and a LWSS-turning reaction which Rott had found in November 1993 (but which was not widely known until Paul Callahan rediscovered it in June 1994) this can be used to prove that there exist {gliderless} guns for LWSS, MWSS and {HWSS} for every period that is a multiple of 46. *..*................................. ....*................................ *...*................................ .****................................ ..................................... ..................................... ..................................... ..................................... ..................................... ...................**..............** ..................**...............** ...................*****............. ..**................****............. ..**.....*........................... ........***.........****............. .......*.*.*.......*****............. ........*..*......**...............** ........***........**..............** .........*........................... ..................................... ..................................... ..................................... ..................................... ..*.......*.......................... ..................................... ***.......***........................ .**.**.**.**......................... ..***...***.......................... ...*.....*........................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..**.....**.......................... ..**.....**.......................... :MW volcano: (p5) Found by Dean Hickerson in April 1992. ......*...... ....*...*.... ............. ...*.....*... .***.***.***. *...**.**...* *.***.*.****. .*........... ...*.*.*.**.* ..**.***.*.** ...*.*..*.... ...*..**..... ..**......... :My Experience with B-heptominos in Oscillators: An article by Dave Buckingham (October 1996) that describes his discovery of {Herschel conduit}s, including sufficient (indeed ample) {stable} conduits to enable, for the first time, the construction of period n oscillators - and true period n guns - for every sufficiently large integer n. (See {Herschel loop} and {emu}.) :natural: Occurring often in random patterns. There is no precise measure of naturalness, since the most useful definition of "random" in this context is open to debate. Nonetheless, it is clear that objects such as {block}s, {blinker}s, {beehive}s and {glider}s are very natural, while {eater2}s, {dart}s, {gun}s, etc., are not. :negentropy: (p2) Compare {Hertz oscillator}. ...**.*.... ...*.**.... ........... ....***.... ...*.*.*.** ...**..*.** **.*...*... **.*...*... ....***.... ........... ....**.*... ....*.**... :neighbour: Any of the eight cells adjacent to a given cell. A cell is therefore not considered to be a neighbour of itself, although the neighbourhood used in Life does in fact include this cell (see {cellular automaton}). :new five: (p3) Found by Dean Hickerson, January 1990. ..**..... .*..*.... .*.*..*.. **.*.**.. *........ .***.**** .....*..* *.**..... **.**.... :new gun: An old name for the second known basic {gun} (found, like the first, by Bill Gosper), shown below. A number of other ways of constructing a gun from two {twin bees shuttle}s have since been found - see {edge shooter} for one of these. .........................**.....** .........................**.....** .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. ...........................**.**.. ..........................*.....*. .................................. .........................*.......* .........................*..*.*..* .........................***...*** .................................. .................................. .................................. .................................. .................*................ **...............**............... **................**.............. .............**..**............... .................................. .................................. .................................. .............**..**............... **................**.......**..... **...............**........**..... .................*................ :Noah's ark: The following diagonal {puffer} consisting of two {switch engine}s. This was found by Charles Corderman in 1971. The name comes from the variety of objects it leaves behind: blocks, blinkers, beehives, loaves, gliders, ships, boats, long boats, beacons and block on tables. ..........*.*.. .........*..... ..........*..*. ............*** ............... ............... ............... ............... ............... .*............. *.*............ ............... *..*........... ..**........... ...*........... See also {ark}. :n-omino: Any {polyomino} with exactly n cells. :non-monotonic: A {spaceship} is said to be non-monotonic if its leading edge falls back in some generations. The first example (shown below) was found by Hartmut Holzwart in August 1992. This is p4 and travels at c/4. In April 1994, Holzwart found examples of p3 spaceships with this property, and this is clearly the smallest possible period. Another non-monotonic spaceship is the {weekender}. ..........**.*....... ......***.*.***...... ..*.*..........*...** **....**.....*...**** ..*.**..*....***.*... ........*....*....... ..*.**..*....***.*... **....**.....*...**** ..*.*..........*...** ......***.*.***...... ..........**.*....... :non-spark: Something that looks like a spark, but isn't. An {OWSS} produces one of these instead of a {belly spark}, and is destroyed by it. :non-standard spaceship: Any {spaceship} other than a {glider}, {LWSS}, {MWSS} or {HWSS}. :obo spark: A {spark} of the form O.O (so called after its {rle} encoding). :octagon II: (p5) The first known p5 {oscillator}, discovered in 1971 independently by Sol Goodman and Arthur Taber. The name is due to the latter. ...**... ..*..*.. .*....*. *......* *......* .*....*. ..*..*.. ...**... :octagon IV: (p4) Found by Robert Wainwright, January 1979. .......**....... .......**....... ................ ......****...... .....*....*..... ....*......*.... ...*........*... **.*........*.** **.*........*.** ...*........*... ....*......*.... .....*....*..... ......****...... ................ .......**....... .......**....... :octomino: Any 8-cell {polyomino}. There are 369 such objects. The word is particularly applied to the following octomino (or its two-generation successor), which is fairly common but lacks a proper name: ..** ..** ***. .*.. :odd keys: (p3) Found by Dean Hickerson, August 1989. See also {short keys} and {bent keys}. ..........*. .*.......*.* *.***..**.*. .*..*..*.... ....*..*.... :omino: = {polyomino} :omniperiodic: A {cellular automaton} is said to be omniperiodic if it has {oscillator}s of all {period}s. It is not known if Life is omniperiodic, although this seems likely. Dave Buckingham's work on Herschel conduits in 1996 (see {My Experience with B-heptominos in Oscillators}) reduced the number of unresolved cases to a finite number. At the time of writing the only periods for which no oscillator is known are 19, 23, 31, 37, 38, 41, 43 and 53. If we insist that the oscillator must contain a cell oscillating at the full period, then 34 and 51 should be added to this list. The most recently achieved periods were all found by Noam Elkies: p49 in August 1999 (a glider loop using p7 {reflector}s built from his new p7 {pipsquirter}), p39 (previously only possible without a p39 cell) in July 2000, and p27 in November 2002. Note that if we were to allow infinite oscillators, then all periods are certainly possible, as any period of 14 or more can be obtained using a {glider} (or {LWSS}) stream. :one-sided spaceship synthesis: A {glider synthesis} of a {spaceship} in which all gliders come from the same side of the spaceship's path. Such syntheses are used extensively in the 17c/45 {Caterpillar}. :onion rings: For each integer n>1 onion rings of order n is a {stable} {agar} of {density} 1/2 obtained by tiling the plane with a certain 4n x 4n pattern. The tile for order 3 onion rings is shown below - the reader should then be able to deduce the form of tiles of other orders. ......****** .****.*....* .*..*.*.**.* .*..*.*.**.* .****.*....* ......****** ******...... *....*.****. *.**.*.*..*. *.**.*.*..*. *....*.****. ******...... :on-off: Any p2 {oscillator} in which all {rotor} cells die from {overpopulation}. The simplest example is a {beacon}. Compare {flip-flop}. :O-pentomino: Conway's name for the following {pentomino}, a {traffic light} {predecessor}, although not one of the more common ones. ***** :orbit: A term proposed by Jason Summers to refer to a natural stabilization of a {puffer}. For example, the {switch engine} has two (known) orbits, the block-laying one and the glider-producing one. :Orion: (c/4 diagonally, p4) Found by Hartmut Holzwart, April 1993. ...**......... ...*.*........ ...*.......... **.*.......... *....*........ *.**......***. .....***....** ......***.*.*. .............* ......*.*..... .....**.*..... ......*....... ....**.*...... .......*...... .....**....... In May 1999, Jason Summers found the following smaller variant: .**.......... **........... ..*.......... ....*....***. ....***....** .....***.*.*. ............* .....*.*..... ....**.*..... .....*....... ...**.*...... ......*...... ....**....... :orphan: Conway's preferred term for a {Garden of Eden}. :oscillator: Any pattern that is a {predecessor} of itself. The term is usually restricted to non-{stable} finite patterns. An oscillator is divided into a {rotor} and a {stator}. See also {omniperiodic}. In general {cellular automaton} theory the term "oscillator" usually covers {spaceship}s as well, but this usage is not normal in Life. :overcrowding: = {overpopulation} :over-exposure: = {underpopulation} :overpopulation: Death of a cell caused by it having more than three {neighbour}s. See also {underpopulation}. :overweight spaceship: = {OWSS} :OWSS: A would-be {spaceship} similar to {LWSS}, {MWSS} and {HWSS} but longer. On its own an OWSS is unstable, but it can be escorted by true spaceships to form a {flotilla}. :Ox: A 1976 novel by Piers Anthony which involves Life. :p: = {period} :p30 shuttle: = {queen bee shuttle} :p46 shuttle: = {twin bees shuttle} :p54 shuttle: (p54) A surprising variant of the {twin bees shuttle} found by Dave Buckingham in 1973. See also {centinal}. **.........................** .*.........................*. .*.*.......*.............*.*. ..**.....*..*.....*......**.. ............*.....**......... ........*..........**........ ........*...**....**......... .........*****............... ............................. .........*****............... ........*...**....**......... ........*..........**........ ............*.....**......... ..**.....*..*.....*......**.. .*.*.......*.............*.*. .*.........................*. **.........................** :p6 shuttle: (p6) The following oscillator found by Nicolay Beluchenko in February 2004. *............. ***........... ...*.......... ..**.......... .............. ......*....... .....****..... ......*..*.... .......***.... .............. ..........**.. ..........*... ...........*** .............* This is {extensible} in more than one way: *........................ ***...................... ...*..................... ..**..................... ......................... ......*.................. .....****................ ......*..*............... .......***............... ......................... ..........***............ ..........*..*........... ...........****.......... .............*........... ......................... .................*....... ................***...... .................*.*..... .................*.*..... ..................**..... .....................**.. .....................*.*. .......................*. .......................** :pair of bookends: = {bookends} :pair of tables: = {table on table} :paperclip: (p1) ..**. .*..* .*.** **.*. *..*. .**.. :parallel grey ship: = {with-the-grain grey ship} :parent: A pattern is said to be a parent of the pattern it gives rise to after one generation. Some patterns have infinitely many parents, but other have none at all (see {Garden of Eden}). :parent cells: The three cells that cause a new cell to be born. :PD: = {pentadecathlon} :pedestle: (p5) .....*..... ....*.*.... .*..**..... .***....... .....***... ...**...*.. ..*....*..* .*.*.*.*.** .*.*...*.*. **.*.*.*.*. *..*....*.. ..*...**... ...***..... .......***. .....**..*. ....*.*.... .....*..... :penny lane: (p4) Found by Dave Buckingham, 1972. ...**.....**... ...*.......*... **.*.......*.** **.*.*****.*.** ....*..*..*.... .....*****..... ............... .......*....... ......*.*...... .......*....... :pentadecathlon: (p15) Found in 1970 by Conway while tracking the history of short rows of cells, 10 cells giving this object, which is the most {natural} {oscillator} of period greater than 3. In fact it is the fifth or sixth most common {oscillator} overall, being about as frequent as the {clock}, but much less frequent than the {blinker}, {toad}, {beacon} or {pulsar}. ..*....*.. **.****.** ..*....*.. The pentadecathlon is the only known oscillator which is a {polyomino} in more than one {phase}. :pentant: (p5) Found by Dave Buckingham, July 1976. **........ .*........ .*.*...... ..**....** .........* .....****. .....*.... ..*...***. ..****..*. .....*.... ....*..... ....**.... :pentaplet: Any 5-cell {polyplet}. :pentapole: (p2) The {barberpole} of length 5. **...... *.*..... ........ ..*.*... ........ ....*.*. .......* ......** :pentoad: (p5) Found by Bill Gosper, June 1977. This is {extensible}: if an eater is moved back four spaces then another {Z-hexomino} can can be inserted. (This extensibility was discovered by Scott Kim.) ...........** ...........*. .........*.*. .........**.. .....**...... ......*...... ......*...... ......**..... ..**......... .*.*......... .*........... **........... :pentomino: Any 5-cell {polyomino}. There are 12 such patterns, and Conway assigned them all letters in the range O to Z, loosely based on their shapes. Only in the case of the {R-pentomino} has Conway's label remained in common use, but all of them can nonetheless be found in this lexicon. :period: The smallest number of generations it takes for an {oscillator} or {spaceship} to reappear in its original form. The term can also be used for a {puffer}, {wick}, {fuse}, {superstring}, stream of {spaceship}s, {factory} or {gun}. In the last case there is a distinction between {true} period and {pseudo} period. There is also a somewhat different concept of period for {wicktrailer}s. :perpendicular grey ship: = {against-the-grain grey ship} :perturb: To change the fate of an object by reacting it with other objects. Typically, the other objects are sparks from {spaceship}s or {oscillator}s, or are {eater}s or impacting spaceships. Perturbations are typically done to turn a {dirty} reaction into a {clean} one, or to change the products of a reaction. In many desirable cases the perturbing objects are not destroyed by the reaction, or else are easily replenished. :perturbation: See {perturb}. :phase: A representative generation of a periodic object such as an {oscillator} or {spaceship}. The number of phases is equal to the {period} of the object. The phases of an object usually repeat in the same cyclic sequence forever, although some {perturbation}s can cause a {phase change}. :phase change: A {perturbation} of a periodic object which causes the object to skip ahead by one or more {phase}s. If the perturbation is repeated indefinitely, this can effectively change the {period} of the object. An example of this, found by Dean Hickerson in November 1998, is shown below. In this example, the period of the {oscillator} would be 7 if the {mold} were removed, but the period is increased to 8 because of the repeated phase changes caused by the mold's {spark}. ..........*.... .........*.**.. ..**.........*. ..*......*..*.* .......*...*..* ******.*....**. *.............. .**.**...**.... ..*.*....*.*... ..*.*......*... ...*.......**.. The following pattern demonstrates a p4 c/2 {spaceship} found by Jason Summers, in which the phase is changed as it deletes a {forward glider}. This phase change allows the spaceship to be used to delete a glider wave produced by a {rake} whose period is 2 (mod 4). ........*........................... .......***.**....................... ......**...*.**..................... .....**..*.....*.................... ......*.....*...*.***............... .....**.....*...*.*..*.............. ...**.*.**....*.*.*...*............. ....*.*..**...........*............. .**.*..*..*.........*............... .**.*.....**.........*.***.......... .*.*.............***.*.*.**......... **.**...........**.*..*.*.*......... ..............**.*...***..**.....**. .............*...*......*........*.* ............*.....*..**.*.**.....*.. ...........*..*.*......*.*.......... ...........*.....**....***.......... .............*..........*........... ..........*.*...........*........... .........**.*.***................... ........*.*.*...*................... .......**.*......................... ......*...*.....**.................. .................................... ......**.**......................... Phase changing reactions have enabled the construction of spaceships having periods that were otherwise unknown, and also allow the construction of period-doubling and period-tripling {convoy}s to easily produce very high period rakes. See also {blinker puffer}. :phi: The following common {spark}. The name comes from the shape in the generation after the one shown here. .***. *...* *...* .***. :phoenix: Any pattern all of whose cells die in every generation, but which never dies as a whole. A {spaceship} cannot be a phoenix, and in fact every finite phoenix eventually evolves into an {oscillator}. The following 12-cell oscillator (found by the MIT group in December 1971) is the smallest known phoenix, and is sometimes called simply "the phoenix". ....*... ..*.*... ......*. **...... ......** .*...... ...*.*.. ...*.... Every known phoenix oscillator has period 2. In January 2000, Stephen Silver showed that a period 3 oscillator cannot be a phoenix. The situation for higher periods is unknown. :pi: = {pi-heptomino} :pi-heptomino: (stabilizes at time 173) A common pattern. The name is also applied to later generations of this object - in a {pi ship}, for example, the pi-heptomino itself never arises. *** *.* *.* :pincers: = {great on-off} :pinwheel: (p4) Found by Simon Norton, April 1970. Compare {clock II}. ......**.... ......**.... ............ ....****.... **.*....*... **.*..*.*... ...*...**.** ...*.*..*.** ....****.... ............ ....**...... ....**...... :pi orbital: (p168) Found by Noam Elkies, August 1995. In this {oscillator}, a {pi-heptomino} is turned ninety degrees every 42 generations. A second pi can be inserted to reduce the period to 84. ..............**....**....**............................... .............*..*.*....*.*..*.............................. .............***..........***.............................. ................**......**................................. ...............*..******..*................................ ...............**........**................................ ........................................................... ........*.............................**..........*........ .......*...***......*.........*.......**.........*.*....... ........*.*****..........***...*........................... ............*...*.....*.*****.*..................*......... ............**....***.....*......................**........ ............**....***....**...................*****........ ...................*.....**...................**.**.....**. .................................................*......*.* .....................................................**.*.* .....................................................*.*.*. .......................................................*... ...................................***.........*.*...*..*.. .......**..........................*..*........*..*.....*.. .......**..............................*.......*.*..*...*.. ...................................*..*.............*...*.. ...................................***..................*.. .....................................................*..*.. ................................................*......*... .............................................**.**...*.*.*. .............................................*****...**.*.* .........*......................................**......*.* ........*.*.....................................*.......**. ........................................................... .**.......*.....................................*.*........ *.*......**......................................*......... *.*.**...*****............................................. .*.*.*...**.**............................................. ...*......*................................................ ..*..*..................................................... ..*........................................................ ..*...*.................................................... ..*...*..*.*......................................**....... ..*.....*..*......................................**....... ..*..*...*.*............................................... ...*....................................................... .*.*.*..................................................... *.*.**..................................................... *.*......*................................................. .**.....**.**...................**.....*................... ........*****...................**....***....**............ ........**......................*.....***....**............ .........*..................*.*****.*.....*...*............ ...........................*...***..........*****.*........ .......*.*.........**.......*.........*......***...*....... ........*..........**.............................*........ ........................................................... ................................**........**............... ................................*..******..*............... .................................**......**................ ..............................***..........***............. ..............................*..*.*....*.*..*............. ...............................**....**....**.............. :pi portraitor: (p32) Found by Robert Wainwright in 1984 or 1985. Compare with {gourmet} and {popover}. ...........**........... ......**.*....*.**...... ......*..........*...... .......**......**....... ....***..******..***.... ....*..*........*..*.... .**.*.*..........*.*.**. .*.*.*............*.*.*. ...*................*... .*..*..............*..*. ....*.......***....*.... *...*.......*.*....*...* *...*.......*.*....*...* ....*..............*.... .*..*..............*..*. ...*................*... .*.*.*............*.*.*. .**.*.*..........*.*.**. ....*..*........*..*.... ....***..******..***.... .......**......**....... ......*..........*...... ......**.*....*.**...... ...........**........... :pipsquirt: = {pipsquirter} :pipsquirter: An {oscillator} that produces a {domino} {spark} that is orientated parallel to the direction from which it is produced (in contrast to domino sparkers like the {pentadecathlon} and {HWSS}, which produce domino sparks perpendicular to the direction of production). The following is a small p6 example found by Noam Elkies in November 1997. .....*......... .....*......... ............... ...*...*....... .***.*.***..... *...**....*.... *.**..**.*.*... .*..**..**.*... ..**..**.*.*.** ....*..*.*.*.** ....****.**.... ........*...... ......*.*...... ......**....... :pi ship: A {growing spaceship} in which the back part consists of a {pi-heptomino} travelling at a speed of 3c/10. The first example was constructed by David Bell. All known pi ships are too large to show here, but the following diagram shows how the pi fuse works. ............*............ ...........*.*........... **........**.**........** **.....................** :piston: (p2) Found in 1971. **.......** *.*..*..*.* ..****..*.. *.*..*..*.* **.......** :pi wave: A line of {pi-heptomino}es stabilizing one another. For example, an infinite line of pi-heptominoes arranged as shown below produces a pi wave that moves at a speed of 3c/10, and leaves no debris. ***...............***...............***...............*** *.*...............*.*...............*.*...............*.* *.*...............*.*...............*.*...............*.* :pixel: = {cell} :plet: = {polyplet} :polyomino: A finite collection of orthogonally connected cells. The mathematical study of polyominoes was initiated by Solomon Golomb in 1953. Conway's early investigations of Life and other cellular automata involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata when the patterns had to be evolved by hand rather than by computer. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life. (Note on spelling: As with "dominoes" the plural may also be spelt without an e. In this lexicon I have followed Golomb in using the longer form.) It is possible for a polyomino to be an {oscillator}. In fact there are infinitely many examples of such polyominoes, namely the {cross} and its larger analogues. The only other known examples are the {block}, the {blinker}, the {toad}, the {star} and (in two different phases) the {pentadecathlon}. A polyomino can also be a {spaceship}, as the {LWSS}, {MWSS} and {HWSS} show. :polyplet: A finite collection of orthogonally or diagonally connected cells. This king-wise connectivity is a more natural concept in Life than the orthogonal connectivity of the {polyomino}. :pond: (p1) .**. *..* *..* .**. :pond on pond: (p1) This term is often used to mean {bi-pond}, but may also be used of the following {pseudo still life}. .**...**. *..*.*..* *..*.*..* .**...**. :popover: (p32) Found by Robert Wainwright in August 1984. Compare with {gourmet} and {pi portraitor}. .....................*.......... .....................*.......... .....................***........ .............**.......**........ .............**..***..**........ ...................***.......... ...................***.......... ..............**................ ..***........*..*............... ..***........*.*................ ***..**...*...*....***.......... .....**...*..................... ....***...*..................... ....*.................**...**... ....*...........***..*..*..**... ........*.......*.*...*.*....... .......*.*......*.*....*........ ...**..*..*................*.... ...**...**.................*.... .....................*...***.... .....................*...**..... ..........***........*...**..*** .................**........***.. ................*..*.......***.. ................*.*............. ..........***....*.............. ..........***................... ........**..***..**............. ........**.......**............. ........***..................... ..........*..................... ..........*..................... :population: The number of ON cells. :P-pentomino: Conway's name for the following {pentomino}, a common {spark}. ** ** *. :PPS: (c/5 orthogonally, p30) A pre-pulsar spaceship. Any of three different p30 c/5 orthogonal {spaceship}s in which a {pre-pulsar} is pushed by a pair of {spider}s. The back sparks of the spaceship can be used to perturb gliders in many different ways, allowing the easy construction of c/5 puffers. The first PPS was found by David Bell in May 1998 based on a p15 pre-pulsar spaceship found by Noam Elkies in December 1997. See also {SPPS} and {APPS}. :pre-beehive: The following common {parent} of the {beehive}. *** *** :pre-block: The following common {parent} of the {block}. Another such pattern is the {grin}. *. ** :precursor: = {predecessor} :predecessor: Any pattern that evolves into a given pattern after one or more generations. :pre-pulsar: A common {predecessor} of the {pulsar}, such as that shown below. This duplicates itself in 15 generations. (It fails, however, to be a true {replicator} because of the way the two copies then interact.) ***...*** *.*...*.* ***...*** A pair of {tub}s can be placed to eat half the pre-pulsar as it replicates; this gives the p30 oscillator {Eureka} where the pre-pulsar's replication becomes a movement back and forth. (See {twirling T-tetsons II} for a variation on this idea.) By other means the replication of the pre-pulsar can be made to occur in just 14 generations as half of it is eaten; this allows the construction of p28 and p29 oscillators, and is in fact the only known method for creating a p29 oscillator. The pre-pulsar is also a vital component of the only known p47 oscillator. See also {PPS}. :pre-pulsar spaceship: See {PPS}. :pressure cooker: (p3) Found by the MIT group in September 1971. Compare {mini pressure cooker}. .....*..... ....*.*.... ....*.*.... ...**.**... *.*.....*.* **.*.*.*.** ...*...*... ...*...*... ....***.... ........... ...*.**.... ...**.*.... :primer: A pattern originally constructed by Dean Hickerson in November 1991 that emits a stream of {LWSS}s representing the prime numbers. Some improvements were found by Jason Summers in October 2005. :protein: (p3) Found by Dave Buckingham, November 1972. ....**....... ....*........ ......*...... ..****.*.**.. .*.....*.*..* .*..**.*.*.** **.*.....*... ...*..**.*... ...*....*.... ....****..... ............. ....**....... ....**....... :pseudo: Opposite of {true}. A {gun} emitting a period n stream of spaceships (or rakes) is said to be a pseudo period n gun if its mechanism oscillates with a period different from n. This period will necessarily be a multiple of n. Pseudo period n glider guns are known to exist for all periods greater than or equal to 14, with smaller periods being impossible. The first pseudo p14 gun was built by Dieter Leithner in 1995. The same distinction between true and pseudo also exists for {puffer}s. :pseudo-barberpole: (p5) Found by Achim Flammenkamp in August 1994. In terms of its minimum {population} of 15 this is the smallest known p5 {oscillator}. ..........** ...........* .........*.. .......*.*.. ............ .....*.*.... ............ ...*.*...... ............ ..**........ *........... **.......... :pseudo-random glider generator: An object which emits a random-looking stream of {glider}s, like the sequence of bits from a pseudo-random number generator. Pseudo-random glider generators contain gliders or other {spaceship}s in a loop with a feedback mechanism which causes later spaceships to interfere with the generation of earlier spaceships. The {period} can be very high, since a loop of n spaceships has 2^n possible states. The first pseudo-random glider generator was built by Bill Gosper. David Bell built the first moving one in 1997, using c/3 {rake}s. :pseudo still life: The strict definition of {still life} rules out such stable patterns as the {bi-block}. In such patterns there are dead cells which have more than 3 neighbours in total, but fewer than 3 in any component still life. These patterns are called pseudo still lifes. Mark Niemiec has enumerated the pseudo still lifes up to 24 bits, and his figures are shown below. ------------- Bits Number ------------- 8 1 9 1 10 7 11 16 12 55 13 110 14 279 15 620 16 1645 17 4067 18 10843 19 27250 20 70637 21 179011 22 462086 23 1184882 24 3068984 ------------- :puffer: An object that moves like a {spaceship}, except that it leaves debris behind. The first known puffers were found by Bill Gosper and travelled at c/2 orthogonally (see diagram below for the very first one, found in 1971). Not long afterwards c/12 diagonal puffers were found (see {switch engine}). Discounting {wickstretcher}s (which are not puffers in the conventional sense), no new velocity was obtained after this until David Bell found the first c/3 orthogonal puffer in April 1996. Since then c/5 orthogonal puffers have also been found, the first by Tim Coe in May 1997. Jason Summers built the first c/4 orthogonal puffer in January 1999, and the first 2c/5 orthogonal puffer in February 1999. Hartmut Holzwart built the first c/4 diagonal puffer (as opposed to a wickstretcher) in February 2004. .***......*.....*......***. *..*.....***...***.....*..* ...*....**.*...*.**....*... ...*...................*... ...*..*.............*..*... ...*..**...........**..*... ..*...**...........**...*.. :puffer engine: A pattern which can be used as the main component of a {puffer}. The pattern may itself be a puffer (e.g. the classic {puffer train}), it may be a spaceship (e.g. the {Schick engine}), or it may even be unstable (e.g. the {switch engine}). :puffer train: The full name for a {puffer}, coined by Conway before any examples were known. The term was also applied specifically to the classic puffer train found by Bill Gosper and shown below. This is very {dirty}, and the tail does not stabilize until generation 5533. It consists of a {B-heptomino} (shown here one generation before the standard form) escorted by two {LWSS}. (This was the second known puffer. The first is shown under {puffer}.) .***...........*** *..*..........*..* ...*....***......* ...*....*..*.....* ..*....*........*. :puff suppressor: An attachment at the back of a {line puffer} that suppresses all or some of its puffing action. The example below (by Hartmut Holzwart) has a 3-cell puff suppressor at the back which suppresses the entire puff, making a p2 {spaceship}. If you delete this puff suppressor then you get a p60 double {beehive} {puffer}. Puff suppressors were first recognised by Alan Hensel in April 1994. ............*.................... ..........**.*................... ..........**...*................. ........*...**.*.....*........... ........****.**...****.......*.*. ......*......*....***.....*.*..*. ......*******...*...*....*..*.... ...*.*......**..*...*.*.**....*.. ..*********.....*..**........*... .**..............*.**.****...*..* **....**.*..........*...*..*.*... .**....*........***......*.*.*..* .........*......**......*....**.. .**....*........***......*.*.*..* **....**.*..........*...*..*.*... .**..............*.**.****...*..* ..*********.....*..**........*... ...*.*......**..*...*.*.**....*.. ......*******...*...*....*..*.... ......*......*....***.....*.*..*. ........****.**...****.......*.*. ........*...**.*.....*........... ..........**...*................. ..........**.*................... ............*.................... :pulsar: (p3) Despite its size, this is the fourth most common {oscillator} (and by far the most common of period greater than 2) and was found very early on by Conway. See also {pre-pulsar} and {pulsar quadrant}. ..***...***.. ............. *....*.*....* *....*.*....* *....*.*....* ..***...***.. ............. ..***...***.. *....*.*....* *....*.*....* *....*.*....* ............. ..***...***.. :pulsar 18-22-20: = {two pulsar quadrants} :pulsar CP 48-56-72: = {pulsar} (The numbers refer to the populations of the three {phase}s.) :pulsar quadrant: (p3) This consists of a quarter of the outer part of a {pulsar} stabilized by a {cis fuse with two tails}. This is reminiscent of {mold} and {jam}. Found by Dave Buckingham in July 1973. See also {two pulsar quadrants}. .....*.. ...***.. ..*...** *..*..*. *...*.*. *....*.. ........ ..***... :pulse: A moving object, such as a {spaceship} or {Herschel}, which can be used to transmit information. See {pulse divider}. Also another name for a {pulsar quadrant}. :pulse divider: A mechanism that lets every n-th object that reaches it pass through, and deletes all the rest, where n > 1 and the objects are typically {spaceship}s or {Herschel}s. The following diagram shows a p5 glider pulse divider by Dieter Leithner (February 1998). The first glider moves the centre block and is reflected at 90 degrees. The next glider to come along will not be reflected, but will move the block back to its original position. The small size and low period of this example make it useful for constructing glider {gun}s of certain periods. p7, p22, p36 and p46 versions of this pulse divider are also known. .....**................... .....**................... .......................... ..................**...... .................*..*..... .................*.*..*..* *...............**.*.***** .**...........*...**...... **...............**..***.. .............*...*.*..*.*. ........**.......**..**.*. ........**....*...**...*.. ................**.*.**... .................*.*.*.... .................*.*..*... ..................*..**... ..**...................... ...*...................... ***....................... *......................... .......................... ............**............ ............*............. .............***.......... ...............*.......... :pulshuttle V: (p30) Found by Robert Wainwright, May 1985. Compare {Eureka}. .............*..............*............. ............*.*.......*....*.*............ .............*......**.**...*............. ......................*................... ..**......**..................**......**.. *....*..*....*..............*....*..*....* *....*..*....*..............*....*..*....* *....*..*....*........*.....*....*..*....* ..**......**........**.**.....**......**.. ......................*................... .......................................... .......................................... ..**......**..................**......**.. *....*..*....*........*.....*....*..*....* *....*..*....*......**.**...*....*..*....* *....*..*....*........*.....*....*..*....* ..**......**..................**......**.. .......................................... .......................................... ......................*................... ..**......**........**.**.....**......**.. *....*..*....*........*.....*....*..*....* *....*..*....*..............*....*..*....* *....*..*....*..............*....*..*....* ..**......**..................**......**.. ......................*................... .............*......**.**...*............. ............*.*.......*....*.*............ .............*..............*............. :pure glider generator: A pattern that evolves into one or more {glider}s, and nothing else. There was some interest in these early on, but they are no longer considered important. Here's a neat example: ..*............ ..*............ ***............ ............... ......***...... .......*....... ............*** ............*.. ............*.. :pushalong: Any {tagalong} at the front of a spaceship. The following is an example (found by David Bell in 1992) attached to the front of a {MWSS}. ..***.*..... .****.*..... **.......... .*.*........ ..****.*.... ...***...... ............ ............ ......*****. ......*....* ......*..... .......*...* .........*.. :pyrotechnecium: (p8) Found by Dave Buckingham in 1972. .......*........ .....*****...... ....*.....*..... .*..*.*.**.*.... *.*.*.*....*..*. .*..*....*.*.*.* ....*.**.*.*..*. .....*.....*.... ......*****..... ........*....... :pyrotechneczum: A common mistaken spelling of {pyrotechnecium}, caused by a copying error in the early 1990s. :python: = {long snake} :Q: = {Quetzal} :Q-pentomino: Conway's name for the following {pentomino}, a {traffic light} {predecessor}. **** ...* :quad: (p2) Found by Robert Kraus, April 1971. Of all {oscillator}s that fit in a 6x6 box this is the only {flipper}. **..** *..*.* .*.... ....*. *.*..* **..** :QuadLife: A form of {colorized Life} in which there are four types of ON cell. A newly-born cell takes the type of the majority of its three {parent cells}, or the remaining type if its parent cells are all of different types. In areas where there are only two types of ON cell QuadLife reduces to {Immigration}. :quadpole: (p2) The {barberpole} of length 4. **..... *.*.... ....... ..*.*.. ....... ....*.* .....** :quapole: = {quadpole} :quarter: (c/4 diagonally, p4) The following 25-cell {spaceship}, found by Jason Summers in September 2000. See also {tubstretcher}. ........**... .......**.... .........*... ...........** ..........*.. ............. .........*..* .**.....**... **.....*..... ..*....*.*... ....**..*.... ....**....... :quasar: (p3) Found by Robert Wainwright, August 1971. See {pulsar}. ..........***...***.......... ............................. ........*....*.*....*........ ........*....*.*....*........ ........*....*.*....*........ ..........***...***.......... ............................. ........***.......***........ ..***..*....*...*....*..***.. .......*....*...*....*....... *....*.*....*...*....*.*....* *....*.................*....* *....*..***.......***..*....* ..***...................***.. ............................. ..***...................***.. *....*..***.......***..*....* *....*.................*....* *....*.*....*...*....*.*....* .......*....*...*....*....... ..***..*....*...*....*..***.. ........***.......***........ ............................. ..........***...***.......... ........*....*.*....*........ ........*....*.*....*........ ........*....*.*....*........ ............................. ..........***...***.......... :queen bee: See {queen bee shuttle}. :queen bee shuttle: (p30) Found by Bill Gosper in 1970. There are a number of ways to stabilize the ends. Gosper originally stabilized shuttles against one another in a square of eight shuttles. Two simpler methods are shown here; for a third see {buckaroo}. The queen bee shuttle is the basis of all known {true} p30 {gun}s (see {Gosper glider gun}). .........*............ .......*.*............ ......*.*............. **...*..*............. **....*.*............. .......*.*........**.. .........*........*.*. ....................*. ....................** :Quetzal: Dieter Leithner's name for the {true} p54 glider gun he built in January 1998. (This is short for {Quetzalcoatlus} and expresses the fact that the gun was a very large {Herschel loop} that was not an {emu}.) Shortly afterwards Leithner also built a p56 Quetzal using a mechanism found by Noam Elkies for this purpose. In October 1998 Stephen Silver constructed a p55 Quetzal using Elkies' p5 {reflector} of the previous month. Some of the more recent Quetzals are not Herschel loops, but are instead short Herschel tracks firing several glider streams all but one of which is reflected back to the beginning of the track to create a new Herschel. Noam Elkies first had the idea of doing this for the p55 case, and Stephen Silver constructed the resulting gun shortly after building the original (much larger) p55 Quetzal. Jason Summers later built a p54 version, which is more complicated because the evenness of the period makes the timing problems considerably more difficult. :Quetzalcoatlus: A giant flying dinosaur after which Dieter Leithner named his p54 gun. Usually abbreviated to {Quetzal}, or simply Q (as in Q54, Q55, Q56, Q-gun, etc.). :quilt: = {squaredance} :R: = {R-pentomino} :R2D2: (p8) This was found, in the form shown below, by Peter Raynham in the early 1970s. The name derives from a form with a larger and less symmetric {stator} discovered by Noam Elkies in August 1994. Compare with {Gray counter}. .....*..... ....*.*.... ...*.*.*... ...*.*.*... **.*...*.** **.*...*.** ...*...*... ...*.*.*... ....*.*.... .....*..... :r5: = {R-pentomino} :rabbits: (stabilizes at time 17331) A 9-cell {methuselah} found by Andrew Trevorrow in 1986. *...*** ***..*. .*..... The following {predecessor}, found by Trevorrow in October 1995, has the same number of cells and lasts two generations longer. ..*....* **...... .**.***. :rake: Any {puffer} whose debris consists of {spaceship}s. A rake is said to be forwards, backwards or sideways according to the direction of the spaceships relative to the direction of the rake. Originally the term "rake" was applied only to forwards c/2 glider puffers (see {space rake}). Many people prefer not to use the term in the case where the puffed spaceships travel parallel or anti-parallel to the puffer, as in this case they do not rake out any significant region of the Life plane (and, in contrast to true rakes, these puffers cannot travel in a stream, and so could never be produced by a {gun}). Although the first rakes (circa 1971) were c/2, rakes of other velocities have since been built. Dean Hickerson's construction of {Cordership}s in 1991 made it easy for c/12 diagonal rakes to be built, although no one actually did this until 1998, by which time David Bell had constructed c/3 and c/5 rakes (May 1996 and September 1997, respectively). Jason Summers constructed a 2c/5 rake in June 2000 (building on work by Paul Tooke and David Bell) and a c/4 orthogonal rake in October 2000 (based largely on reactions found by David Bell). The smallest possible period for a rake is probably 7, as this could be achieved by a 3c/7 orthogonal backwards glider puffer. The smallest period attained to date is 8 (Jason Summers, March 2001) - see {backrake}. :$rats: (p6) Found by Dave Buckingham, 1972. .....**..... ......*..... ....*....... **.*.****... **.*.....*.* ...*..***.** ...*....*... ....***.*... .......*.... ......*..... ......**.... :R-bee: = {bun} :receiver: See {Herschel receiver}. :reflector: Any {stable} or oscillating pattern that can reflect some type of {spaceship} (usually a {glider}) without suffering permanent damage. The first known reflector was the {pentadecathlon}, which functions as a 180-degree glider reflector (see {relay}). Other examples include the {buckaroo}, the {twin bees shuttle} and some oscillators based on the {traffic jam} reaction. Glider {gun}s can also be made into reflectors, although these are mostly rather large. In September 1998 Noam Elkies found some fast small-period glider reflectors. The p8 version is shown below. Replacing the {figure-8} by the p6 {pipsquirter} gives a p6 version. A more complicated construction allows a p5 version (which, as had been anticipated, soon led to a {true} p55 gun - see {Quetzal}). And in August 1999 Elkies found a suitable p7 {sparker}, allowing the first p49 oscillator to be constructed. ......**.....**.. *.*...**.....*... .**........*.*... .*.........**.... .......**........ .......*.*....... ........*........ ................. ...........***... ...........***... ...........***... ..............*** ..............*** ..............*** Stable reflectors are special in that if they satisfy certain conditions they can be used to construct {oscillator}s of all sufficiently large periods. It was known for some time that stable reflectors were possible (see {universal constructor}), but no one was able to construct an explicit example until Paul Callahan did so in October 1996. All known stable reflectors are very slow. Callahan's original reflector has a {repeat time} of 4840, soon improved to 1686 and then 894 and then 850. In November 1996 Dean Hickerson found a variant in which this is reduced to 747. Dave Buckingham reduced it to 672 in May 1997 using a somewhat different method, and in October 1997 Stephen Silver reduced it to 623 by a method closer to the original. In November 1998 Callahan reduced this to 575 with a new initial reaction. A small modification by Silver a few days later brought this down to 497. But in April 2001 Dave Greene found a 180-degree stable reflector with a repeat time of only 202 (see {boojum reflector}). This reflector also won the $100 prize that Dieter Leithner had offered in April 1997 for the first stable reflector to fit in a 50x50 box, and the additional $100 that Alan Hensel had offered in January 1999 for the same feat. Dave Greene has subsequently offered $50 for the first 90-degree stable glider reflector that fits in a 50x50 box, and a further $50 for the first in a 35x35 box. See also {glider turner}. :regulator: An object which converts input {glider}s aligned to some period to output gliders aligned to a different period. The most interesting case is a {universal regulator}. :relay: Any {oscillator} in which {spaceship}s (typically {glider}s) travel in a loop. The simplest example is the p60 one shown below using two {pentadecathlon}s. Pulling the pentadecathlons further apart allows any period of the form 60+120n to be achieved - this is the simplest proof of the existence of oscillators of arbitrarily large period. ...........................*....*.. ................**.......**.****.** .................**........*....*.. ................*.................. ..*....*........................... **.****.**......................... ..*....*........................... :repeater: Any {oscillator} or {spaceship}. :repeat time: The minimum number of generations that is possible between the arrival of one object and the arrival of the next. This term is used for things such as {reflector}s or {conduit}s and the objects (gliders or Herschels, for example) will interact fatally with each other (or one will interact fatally with a disturbance caused by the other) if they are too close together. For example, the repeat time of Dave Buckingham's 59-step B-heptomino to Herschel conduit (shown under {conduit}) is 58. :rephaser: The following reaction that shifts the phase and path of a pair of gliders. There is another form of this reaction that reflects the gliders 180 degrees - see {glider-block cycle}. ..*..*.. *.*..*.* .**..**. ........ ........ ...**... ...**... :replicator: A finite pattern which repeatedly creates copies of itself. Such objects are known to exist (see {universal constructor}), but no concrete example is known. :reverse fuse: A {fuse} that produces some initial debris, but then burns {clean}ly. The following is a simple example. .............** ............*.* ...........*... ..........*.... .........*..... ........*...... .......*....... ......*........ .....*......... ....*.......... ...*........... ..*............ **............. :revolver: (p2) *............* ***....*...*** ...*.*.*..*... ..*......*.*.. ..*.*......*.. ...*..*.*.*... ***...*....*** *............* :ring of fire: (p2) The following {muttering moat} found by Dean Hickerson in September 1992. ................*................. ..............*.*.*............... ............*.*.*.*.*............. ..........*.*.*.*.*.*.*........... ........*.*.*..**.*.*.*.*......... ......*.*.*.*......*..*.*.*....... ....*.*.*..*..........*.*.*.*..... .....**.*..............*..*.*.*... ...*...*..................*.**.... ....***....................*...*.. ..*.........................***... ...**...........................*. .*...*........................**.. ..****.......................*...* *.............................***. .***.............................* *...*.......................****.. ..**........................*...*. .*...........................**... ...***.........................*.. ..*...*....................***.... ....**.*..................*...*... ...*.*.*..*..............*.**..... .....*.*.*.*..........*..*.*.*.... .......*.*.*..*......*.*.*.*...... .........*.*.*.*.**..*.*.*........ ...........*.*.*.*.*.*.*.......... .............*.*.*.*.*............ ...............*.*.*.............. .................*................ :rle: Run-length encoded. Run-length encoding is a simple (but not very efficient) method of file compression. In Life the term refers to a specific ASCII encoding used for Life patterns (and patterns for other similar cellular automata). This encoding was introduced by Dave Buckingham and is now the usual means of exchanging Life patterns (especially large ones) by e-mail. :rock: Dean Hickerson's term for an {eater} which remains intact throughout the eating process. The {snake} in Dave Buckingham's 59-step B-to-Herschel conduit (shown under {conduit}) is an example. Other still lifes that sometimes act as rocks include the {tub}, the {hook with tail}, the {eater1} (eating with its tail) and the {hat} (in Heinrich Koenig's stabilization of the {twin bees shuttle}). :roteightor: (p8) Found by Robert Wainwright in 1972. .*............ .***........** ....*.......*. ...**.....*.*. ..........**.. .............. .....***...... .....*..*..... .....*........ ..**..*...*... .*.*......*... .*.......*.... **........***. ............*. :rotor: The cells of an {oscillator} that change state. Compare {stator}. It is easy to see that any rotor cell must be adjacent to another rotor cell. :R-pentomino: This is by far the most active {polyomino} with less than six cells: all the others stabilize in at most 10 generations, but the R-pentomino does not do so until generation 1103, by which time it has a {population} of 116. .** **. .*. :rule 22: Wolfram's rule 22 is the 2-state 1-D {cellular automaton} in which a cell is ON in the next generation if and only if exactly one of its three neighbours is ON in the current generation (a cell being counted as a neighbour of itself). This is the behaviour of Life on a cylinder of width 1. :ruler: A pattern constructed by Dean Hickerson in May 2005 that produces a stream of {LWSS} with gaps in it, such that the number of LWSS between successive gaps follows the "ruler function" (sequence A001511 in The On-Line Encyclopedia of Integer Sequences). :rumbling river: Any {oscillator} in which the {rotor} is connected and contained in a strip of width 2. The following p3 example is by Dean Hickerson, November 1994. ..............**......**......**...*.**.......... ....*........*..*....*..*....*..*..**.*.......... *..*.*....*...**..*...**..*...*.*.....*.**....... ****.*..******..******..******..******.*.*....... .....*.*.....*.*.....*.*.....*.*.....*.*......**. ..**.*.*.*.*...*.*.*...*.*.*...*.*.*...*.*.....*. .*.....*.*...*.*.*...*.*.*...*.*.*...*.*.*.*.**.. .**......*.*.....*.*.....*.*.....*.*.....*.*..... .......*.*.******..******..******..******..*.**** .......**.*.....*.*...*..**...*..**...*....*.*..* ..........*.**..*..*....*..*....*..*........*.... ..........**.*...**......**......**.............. :S: Usually means {big S}, but may sometimes mean {paperclip}. :sailboat: (p16) A {boat} {hassle}d by a {Kok's galaxy}, a {figure-8} and two {eater3}s. Found by Robert Wainwright in June 1984. ........*...........*........ .......*.*.........*.*....... ........*...........*........ ............................. ......*****.......*****...... .....*....*.......*....*..... ....*..*.............*..*.... .*..*.**.............**.*..*. *.*.*.....*.......*.....*.*.* .*..*....*.*.....*.*....*..*. ....**..*..*.....*..*..**.... .........**.......**......... .............**.............. .............*.*............. ........*..*..*.............. .......*..................... .....**..........***......... ..*......**.*....***......... .....*...*..*....***......... .....***.*...*......***...... ..*...........*.....***...... ...*...*.***........***...... ....*..*...*................. ....*.**......*.............. ..........**................. .........*................... .....*..*.................... :sawtooth: Any finite pattern whose {population} grows without bound but does not tend to infinity. (In other words, the population reaches new heights infinitely often, but also infinitely often returns to some fixed value.) Conway's preferred plural is "sawteeth". The first sawtooth was constructed by Dean Hickerson in April 1991. The least infinitely repeating population of any known sawtooth is 262 (David Bell, July 2005). See also {tractor beam}. :SBM: = {sliding block memory} :Schick engine: (c/2 orthogonally, p12) This {spaceship}, found by Paul Schick in 1972, produces a large {spark} (the 15 live cells at the rear in the {phase} shown below) which can be {perturb}ed by other c/2 spaceships to form a variety of {puffer}s. The diagram below shows the smallest form of the Schick engine, using two {LWSS}. It is also possible to use two {MWSS} or two {HWSS}, or even a LWSS and a HWSS. ****.............. *...*.........*... *...........**.... .*..*..**.....***. ......***......*** .*..*..**.....***. *...........**.... *...*.........*... ****.............. :Schick ship: = {Schick engine} :scorpion: (p1) ...*... .***... *...**. *.*.*.* .**.*.* .....*. :scrubber: (p2) Found in 1971. ....*...... ..***...... .*......... .*..***.... **.*...*... ...*...*... ...*...*.** ....***..*. .........*. ......***.. ......*.... :SE: = {switch engine} :seal: (c/6 diagonally, p6) The first c/6 diagonal {spaceship}, found by Nicolay Beluchenko in September 2005. ...*..**.......................... .***.*.*.*........................ .*..***..**....................... *..******.*.***................... .*..***.*.*****................... ......*.*.*.*..................... *.*...*.*.*****................... *..*.*..*.**...*.................. ...*..**.......***................ .*...*****.***..**................ ....*.........*................... ..*.*.........*................... ....**.*****...*.................. ......*.***..*.....**............. ......*..*...*.***.**............. ........**...***.*..*...*......... ........**....**.****...***....... ...................*.*..*......... .............*.*.....**..**....... .............*..*.....*.***.....*. .............*...*....**..*...*..* ...............***.....**........* ...............*.*..*..*.....**..* .................*..**.**.*..*.... ................*.......*.*....... .................*...****......... ..................*...*........... .................................. .......................*.......... ......................*.*......... .....................**........... .....................*.*.......... .....................**........... .......................*.......... ......................*........... :second glider domain: The second glider domain of an {edge shooter} is the set of displacements (in space and time, relative to the glider stream emitted by the edge shooter) that a glider stream may have without interfering with the edge shooter. This is useful to know, because edge shooters are often used to generate glider streams very close to other glider streams. :sesquihat: (p1) Halfway between a {hat} and a {twinhat}. ....* **.*.*. .*.*.*. .*.*.** ..*... :SGR: Abbreviation for {stable} {glider} {reflector}. :shillelagh: (p1) **... *..** .**.* :ship: (p1) The term is also used as a synonym of {spaceship}. **. *.* .** :ship in a bottle: (p16) Found by Bill Gosper in August 1994. See also {bottle}. ....**......**.... ...*..*....*..*... ...*.*......*.*... .**..***..***..**. *......*..*......* *.**..........**.* .*.*..........*.*. ...**...**...**... .......*.*........ .......**......... ...**........**... .*.*..........*.*. *.**..........**.* *......*..*......* .**..***..***..**. ...*.*......*.*... ...*..*....*..*... ....**......**.... :ship on boat: = {ship tie boat} :ship on ship: = {ship-tie} :ship-tie: (p1) The name is by analogy with {boat-tie}. **.... *.*... .**... ...**. ...*.* ....** :ship tie boat: (p1) **.... *.*... .**... ...**. ...*.* ....*. :short keys: (p3) Found by Dean Hickerson, August 1989. See also {bent keys} and {odd keys}. .*........*. *.***..***.* .*..*..*..*. ....*..*.... :shuttle: Any {oscillator} which consists of an active region moving back and forth between stabilizing objects. The most well-known examples are the {queen bee shuttle} (which has often been called simply "the shuttle") and the {twin bees shuttle}. See also {p54 shuttle} and {Eureka}. Another example is the p72 {R-pentomino} shuttle that forms part of the pattern given under {factory}. :siamese: A term used in naming certain {still life}s (and the {stator} part of certain {oscillator}s). It indicates that the object consists of two smaller objects sharing two or more cells. See {snake siamese snake} and {loaf siamese barge} for examples. :side: Half a {sidewalk}. In itself this is unstable and requires an {induction coil}. **... *.*** ....* :sidecar: A small {tagalong} for a {HWSS} that was found by Hartmut Holzwart in 1992. The resulting {spaceship} (shown below) has a {phase} with only 24 cells, making it in this respect the smallest known spaceship other than the {standard spaceship}s and some trivial two-spaceship {flotilla}s derived from them. Note also that a HWSS can support two sidecars at once. .*...... *.....*. *.....*. *****.*. ........ ....**.. ..*....* .*...... .*.....* .******. :side-shooting gun: = {slide gun} :side-tracking: See {universal constructor}. :sidewalk: (p1) .**.** ..*.*. .*..*. .*.*.. **.**. :siesta: (p5) Found by Dave Buckingham in 1973. Compare {sombreros}. ...........**... ...**.....*.*... ...*.*....*..... .....*...**.*... ...*.**.....***. .***.....*.*...* *...*.*.....***. .***.....**.*... ...*.**...*..... .....*....*.*... ...*.*.....**... ...**........... :signal: Movement of information through the Life universe. Signals can be carried by {spaceship}s, {fuse}s, {drifter}s, or {conduit}s. Spaceships can only transfer a signal at the speed of the spaceship, while fuses can transfer a signal at speeds up to the {speed of light}. In practice, many signals are encoded as the presence or absence of a {glider} (or other spaceship) at a particular point at a particular time. Such signals can be combined by the collision of gliders to form logic operations such as AND, OR, and NOT gates. Signals can be duplicated using {glider duplicator}s or other {fanout} devices, and can be used up by causing {perturbation}s on other parts of the Life object. Signals are used in {pseudo-random glider generator}s, the {unit Life cell} and the {Fermat prime calculator}, among others. :Silver's p5: (p5) The following oscillator found by Stephen Silver in February 2000: **......... *.......... .*..*...... ...**...... ...*...*.** ..*....**.* ..**....... As this has no {spark}, it appears useless. Nonetheless, in March 2000, David Eppstein found a way to use it to reduce the size of Noam Elkies' p5 {reflector}. :singular flip flop: (p2) Found by Robert Wainwright, July 1972. ..*... ..*.*. *....* ****** ...... ..**.. ..**.. :sinking ship: = {canoe} :six Ls: (p3) This is a compact form of {loading dock}. ...*... .***..* *...*** ***.... ....*** ***...* *..***. ...*... :sixty-nine: (p4) Found by Robert Wainwright, October 1978. .........*........... ........*.*.......... ..................... ......*...**......... .....*.....*......... ......*.*............ ........**......*.... ................*.... ..*.....**....***.... ..*...........**..... ***.......**..**..*** **......*.**....***.. **..***.*.*.....***.. ..***................ ..***......*......... ..........*.*........ ..................... ........*...**....... .......*.....*....... ........*.*.......... ..........**......... :skewed quad: (p2) .**.... .*...** ..*.*.* ....... *.*.*.. **...*. ....**. :skewed traffic light: (p3) Found by Robert Wainwright, August 1989. .............**......... ............*..*........ .............*.*........ .........**...*......... ..........*.**.......... ............*........... ............*........... ........................ **........***......*.... ****.*........*...**.... *.*..***.*....*......... .........*....*.***..*.* ....**...*........*.**** ....*......***........** ........................ ...........*............ ...........*............ ..........**.*.......... .........*...**......... ........*.*............. ........*..*............ .........**............. :slide gun: A {gun} which fires sideways from an extending arm. The arm consists of streams of {spaceship}s which are pushing a pattern away from the body of the gun and releasing an output spaceship every time they do so. Each output spaceship therefore travels along a different path. Dieter Leithner constructed the first slide gun in July 1994 (although he used the term "side shooting gun"). The following pattern shows the key reaction of this slide gun. The three gliders shown will push the block one cell diagonally, thereby extending the length of the arm by one cell, and at the same time they release an output glider sideways. (In 1999, Jason Summers constructed slide guns using other reactions.) ..............**. ..............**. ........***...... ..........*...... .........*.....** ..............*.* ................* ................. ................. ................. ................. ................. ................. ................. ................. ................. ................. .*............... .**.............. *.*.............. :sliding block memory: A memory register whose value is stored as the position of a {block}. The block can be moved by means of {glider} collisions - see {block pusher} for an example. In Conway's original formulation (as part of his proof of the existence of a {universal computer} in Life) 2 gliders were used to pull the block inwards by three diagonal spaces, and 30 gliders were used to push it out by the same amount. Dean Hickerson later greatly improved on this, finding a way to pull a block inwards by one diagonal space using 2 gliders, and push it out using 3 gliders. In order for the memory to be of any use there also has to be a way to read the value held. It suffices to be able to check whether the value is zero (as Conway did), or to be able to detect the transition from one to zero (as Hickerson did). Dean Hickerson's sliding block memory is used in Paul Chapman's {URM}. :slow glider construction: Construction an object by a "slow salvo" of {glider}s all coming from the same direction, in such a way that timing of the gliders does not matter as long as they are not too close behind one another. This type of construction requires an initial seed object, such as a {block}, which is modified by each glider in turn until the desired object is produced. In May 1997, Nick Gotts produced a slow glider construction of a block-laying switch engine from a block, using a slow salvo of 53 gliders. Constructions like this are important in the study of {sparse Life}, as they will occur naturally as gliders created in the first few generations collide with {blonk}s and other debris. Slow glider constructions are also useful in some designs for {universal constructor}s. However, in this case the above definition is usually too restrictive, and it is desirable to allow constructions in which some gliders in the salvo are required to have a particular timing modulo 2 (a "p2 slow salvo"). This gives much greater flexibility, as {blinker}s can now be freely used in the intermediate construction steps. :slow salvo: See {slow glider construction}. :small fish: = {LWSS} :small lake: (p1) See also {lake}. ....*.... ...*.*... ...*.*... .**...**. *.......* .**...**. ...*.*... ...*.*... ....*.... :smiley: (p8) Found by Achim Flammenkamp in July 1994 and named by Alan Hensel. **.*.** ...*... *.....* .*****. ....... ....... ***.*** :SMM breeder: See {breeder}. :smoke: Debris which is fairly long-lived but eventually dies completely. Basically, a large {spark}. This term is used especially when talking about the output from a {spaceship} - see {smoking ship}. :smoking ship: A {spaceship} which produces {smoke}. If the smoke extends past the edge of the rest of the spaceship, then it can be used to perturb other objects as the spaceship passes by. Running gliders into the smoke is often a good way to turn or duplicate the them, or convert them into other objects. Sometimes the smoke from a smoking ship may itself be perturbed by accompanying spaceships in order to form a {puffer}. A simple example of a smoking ship is the {Schick engine}. :snacker: (p9) Found by Mark Niemiec in 1972. This is a {pentadecathlon} with stabilizers which force it into a lower period. **................** .*................*. .*.*............*.*. ..**............**.. .......*....*....... .....**.****.**..... .......*....*....... ..**............**.. .*.*............*.*. .*................*. **................** The stabilizers make the {domino} spark largely inaccessible, but the snacker is {extensible}, as shown in the next diagram, and so a more accessible p9 domino spark can be obtained. In April 1998 Dean Hickerson found an alternative stabilizer that is less obtrusive than the original one, and this is also shown in this diagram. **................................ .*................................ .*.*.........................**... ..**.......................*..*... .......*....*..............***.... .....**.****.**...*....*......***. .......*....*...**.****.**...*...* ..**..............*....*......***. .*.*.......................***.... .*.........................*..*... **...........................**... An end can also be stabilized by killer {candlefrobra}s, although this isn't efficient. :snail: (c/5 orthogonally, p5) The first known c/5 {spaceship}, discovered by Tim Coe in January 1996. For some time it was the slowest known orthogonal spaceship. .*.................................... .*.................................... *..................................... .***.................***...***........ .**.*.........*...*.*......***........ ..*...........**.*.......*....****.... ......*......*...*.*...**.*.....**.... ...*..*.***...**.........*........**.* ...**.*.....*.....*.................*. .........*.*******.................... ...................................... .........*.*******.................... ...**.*.....*.....*.................*. ...*..*.***...**.........*........**.* ......*......*...*.*...**.*.....**.... ..*...........**.*.......*....****.... .**.*.........*...*.*......***........ .***.................***...***........ *..................................... .*.................................... .*.................................... :snake: (p1) **.* *.** :snake bit: An alternative name for a {boat-bit}. Not a very sensible name, because various other things can be used instead of a snake. :snake bridge snake: (p1) ....** ....*. .....* ....** **.*.. *.**.. :snake dance: (p3) Found by Robert Wainwright, May 1972. ...**.*.. ...*.**.. **.*..... .*..*.*** *..*.*..* ***.*..*. .....*.** ..**.*... ..*.**... :snake pit: This term has been used for two different {oscillator}s: the p2 snake pit (essentially the same as {fore and back}) *.**.** **.*.*. ......* ***.*** *...... .*.*.** **.**.* and the p3 snake pit. .....**.... ....*..*... ....*.**... .**.*...... *.*.*.****. *.........* .****.*.*.* ......*.**. ...**.*.... ...*..*.... ....**..... :snake siamese snake: (p1) **.**.* *.**.** :sombrero: One half of {sombreros} or {siesta}. :sombreros: (p6) Found by Dave Buckingham in 1972. If the two halves are moved three spaces closer to one another then the period drops to 4, and the result is just a less compact form of {Achim's p4}. Compare also {siesta}. ...**........**... ...*.*......*.*... .....*......*..... ...*.**....**.*... .***..........***. *...*.*....*.*...* .***..........***. ...*.**....**.*... .....*......*..... ...*.*......*.*... ...**........**... :soup: A random initial pattern, often assumed to cover the whole Life universe. :space dust: A part of a {spaceship} or {oscillator} which looks like a random mix of ON and OFF cells. It is usually very difficult to find a {glider synthesis} for an object that consists wholly or partly of space dust. :spacefiller: Any pattern that grows at a quadratic rate by filling space with an {agar}. The first example was found in September 1993 by Hartmut Holzwart, following a suggestion by Alan Hensel. The diagram below shows a smaller spacefiller found by Tim Coe. See also {Max}. Spacefillers can be considered as {breeder}s (more precisely, MMS breeders), but they are very different from ordinary breeders. The word "spacefiller" was suggested by Harold McIntosh and soon became the accepted term. ..................*........ .................***....... ............***....**...... ...........*..***..*.**.... ..........*...*.*..*.*..... ..........*....*.*.*.*.**.. ............*....*.*...**.. ****.....*.*....*...*.***.. *...**.*.***.**.........**. *.....**.....*............. .*..**.*..*..*.**.......... .......*.*.*.*.*.*.....**** .*..**.*..*..*..**.*.**...* *.....**...*.*.*...**.....* *...**.*.**..*..*..*.**..*. ****.....*.*.*.*.*.*....... ..........**.*..*..*.**..*. .............*.....**.....* .**.........**.***.*.**...* ..***.*...*....*.*.....**** ..**...*.*....*............ ..**.*.*.*.*....*.......... .....*.*..*.*...*.......... ....**.*..***..*........... ......**....***............ .......***................. ........*.................. :space rake: The following p20 forwards glider {rake}, which was the first known rake. It consists of an {ecologist} with a {LWSS} added to turn the dying debris into {glider}s. ...........**.....**** .........**.**...*...* .........****........* ..........**.....*..*. ...................... ........*............. .......**........**... ......*.........*..*.. .......*****....*..*.. ........****...**.**.. ...........*....**.... ...................... ...................... ...................... ..................**** *..*.............*...* ....*................* *...*............*..*. .****................. :spaceship: Any finite pattern that reappears (without additions or losses) after a number of generations and displaced by a non-zero amount. By far the most {natural} spaceships are the {glider}, {LWSS}, {MWSS} and {HWSS}. For further examples see {B29}, {big glider}, {brain}, {Canada goose}, {Coe ship}, {Cordership}, {crane}, {dart}, {dragon}, {ecologist}, {edge-repair spaceship}, {Enterprise}, {flotilla}, {fly}, {hammerhead}, {hivenudger}, {non-monotonic}, {Orion}, {puff suppressor}, {pushalong}, {quarter}, {Schick engine}, {seal}, {sidecar}, {snail}, {still life tagalong}, {sparky}, {swan}, {turtle}, {wasp}, {weekender} and {x66}. See also {Caterpillar}. It is known that there exist spaceships travelling in all rational directions and at arbitrarily slow speeds (see {universal constructor}). Before 1989, however, the only known examples travelled at c/4 diagonally (gliders) or c/2 orthogonally (everything else). In 1989 Dean Hickerson started to use automated searches to look for new spaceships, and had considerable success. Other people have continued these searches using tools such as {lifesrc} and {gfind}, and as a result we now have a great variety of spaceships travelling at twelve different velocities. The following table details the discovery of spaceships with new velocities. ----------------------------------------------------- Speed Direction Discoverer Date ----------------------------------------------------- c/4 diagonal Richard Guy 1970 c/2 orthogonal John Conway 1970 c/3 orthogonal Dean Hickerson Aug 1989 c/4 orthogonal Dean Hickerson Dec 1989 c/12 diagonal Dean Hickerson Apr 1991 2c/5 orthogonal Dean Hickerson Jul 1991 c/5 orthogonal Tim Coe Jan 1996 2c/7 orthogonal David Eppstein Jan 2000 c/6 orthogonal Paul Tooke Apr 2000 c/5 diagonal Jason Summers Nov 2000 17c/45 orthogonal Gabriel Nivasch et al. Dec 2004 c/6 diagonal Nicolay Beluchenko Sep 2005 ----------------------------------------------------- A period p spaceship that displaces itself (m,n) during its period, where m>=n, is said to be of type (m,n)/p. It was proved by Conway in 1970 that p>=2m+2n. (This follows immediately from the easily-proved fact that a pattern cannot advance diagonally at a rate greater than one half diagonal step every other generation.) The following diagram shows one of only two known c/5 diagonal spaceships. It was found by Jason Summers in January 2005. ..........**.......... .........*..*......... ........**............ .........*.**......... ..........*.***....... ..........**.***...... ............*....**... ............***....**. ..*.........*.*....... .***........*..*...... *...**................ *..*.*.......**.*..*.. .*.**.****...*...****. ....**.*...**.......*. ....**.**..*.........* .....*...*........*.** ...........*.......*.. ......*.....*......*.. ......*.....*..*...... .......*...**...**.... .......*....**.*...... ..............**...... :Spaceships in Conway's Life: A series of articles posted by David Bell to the newsgroup comp.theory.cell-automata during the period August-October 1992 that described many of the new {spaceship}s found by himself, Dean Hickerson and Hartmut Holzwart. Bell produced an addendum covering more recent developments in 1996. :spark: A pattern that dies. The term is typically used to describe a collection of cells periodically thrown off by an {oscillator} or {spaceship}, but other dying patterns, particularly those consisting or only one or two cells (such as produced by certain glider collisions, for example), are also described as sparks. For examples of small sparks see {unix} and {HWSS}. For an example of a much larger spark see {Schick engine}. :spark coil: (p2) Found in 1971. **....** *.*..*.* ..*..*.. *.*..*.* **....** :sparker: An {oscillator} or {spaceship} that produces {spark}s. These can be used to {perturb} other patterns without being themselves affected. :sparky: A certain c/4 {tagalong}, shown here attached to the back of a {spaceship}. ..........*.................... ..........*...............**... ......**.*.***..........**...*. *.**.**.**..*.*...**.****...... *...**..*.**..***..*.**..**...* *.**....***.*.***......**..*... ........**.*...............*..* *.**....***.*.***......**..*... *...**..*.**..***..*.**..**...* *.**.**.**..*.*...**.****...... ......**.*.***..........**...*. ..........*...............**... ..........*.................... :sparse Life: This refers to the study of the evolution of a Life universe which starts off as a random {soup} of extremely low density. Such a universe is dominated at an early stage by {block}s and {blinker}s (often referred to collectively as {blonk}s) in a ratio of about 2:1. Much later it will be dominated by simple {infinite growth} patterns (presumably mostly {switch engine}s). The long-term fate of a sparse Life universe is less certain. It may possibly become dominated by self-reproducing patterns (see {universal constructor}), but it is not at all clear that there is any mechanism for these to deal with the all junk produced by switch engines. :speed of light: A speed of one cell per generation, the greatest speed at which any effect can propagate. :S-pentomino: Conway's name for the following {pentomino}, which rapidly dies. ..** ***. :spider: (c/5 orthogonally, p5) This is the smallest known c/5 {spaceship}, and was found by David Bell in April 1997. Its side {spark}s have proved very useful in constructing c/5 {puffer}s, including {rake}s. See also {pre-pulsar}. ......*...***.....***...*...... ...**.*****.**...**.*****.**... .*.**.*.....*.*.*.*.....*.**.*. *...*.*...*****.*****...*.*...* ....***.....**...**.....***.... .*..*.***.............***.*..*. ...*.......................*... :spiral: (p1) Found by Robert Wainwright in 1971. **....* .*..*** .*.*... ..*.*.. ...*.*. ***..*. *....** :SPPS: (c/5 orthogonally, p30) The symmetric {PPS}. The original PPS found by David Bell in May 1998. Compare {APPS}. :squaredance: The p2 {agar} formed by tiling the plane with the following pattern. Found by Don Woods in 1971. **...... ....**.. ..*....* ..*....* ....**.. **...... ...*..*. ...*..*. :squirter: = {pipsquirter} :S-spiral: = {big S} :stable: A pattern is said to be stable if it is a {parent} of itself. See {still life}. :stairstep hexomino: (stabilizes at time 63) The following {predecessor} of the {blockade}. ..** .**. **.. :stamp collection: A collection of {oscillator}s (or perhaps other Life objects) in a single diagram, displaying the exhibits much like stamps in a stamp album. The classic examples are by Dean Hickerson (see {http://www.math.ucdavis.edu/~dean/RLE/stamps.html}). :standard spaceship: A {glider}, {LWSS}, {MWSS} or {HWSS}. These have all been known since 1970. :star: (p3) Found by Hartmut Holzwart, February 1993. .....*..... ....***.... ..***.***.. ..*.....*.. .**.....**. **.......** .**.....**. ..*.....*.. ..***.***.. ....***.... .....*..... :star gate: A device by Dieter Leithner (October 1996) for transporting a {LWSS} faster than the {speed of light}. The key reaction is the {Fast Forward Force Field}. :stator: The cells of an {oscillator} that are always on. Compare {rotor}. (The stator is sometimes taken to include also some of those cells which are always off.) The stator is divided into the {bushing} and the {casing}. By analogy, the cells of an {eater} that remain on even when the eater is eating are considered to constitute the stator of the eater. This is not necessarily well-defined, because the eater may have more than one eating action. :step: Another term for a {generation}. This term is particularly used in describing {conduit}s. For example, a 64-step conduit is one through which the active object takes 64 generations to pass. :stillater: (p3) Found by Robert Wainwright, September 1985. This is one of only three essentially different p3 {oscillator}s with only three cells in the {rotor}. The others are {1-2-3} and {cuphook}. ...*.... ..*.*.** ..*.**.* **...... .*.*.**. .*.*..*. ..*..*.. ...**... :still life: Any {stable} pattern, usually assumed to be finite and nonempty. For the purposes of enumerating still lifes this definition is, however, unsatisfactory because, for example, any pair of blocks would count as a still life, and there would therefore be an infinite number of 8-bit still lifes. For this reason a stricter definition is often used, counting a stable pattern as a single still life only if its {island}s cannot be divided into two nonempty sets both of which are stable in their own right. Compare {pseudo still life}. The requirement that a still life not be decomposable into two separate stable patterns may seem a bit arbitrary, as it does not rule out the possibility that it might be decomposable into more than two. This is shown by the patterns in the following diagram, both found by Gabriel Nivasch in July 2001. On the left is a 32-cell pattern that can be broken down into three stable pieces but not into two. On the right is a 34-cell pattern that can be broken down into four stable pieces but not into two or three. (Note that, as a consequence of the Four-Colour Theorem, four is as high as you need ever go.) It is arguable that patterns like these ought not to be considered as single still lifes. ......**...........**. ..*.*..*......**.*..*. .*.**.*.......*.**.*.. .*....**...........**. **.**.........*.**...* ...**.**....***.**.**. **....*....*.......*.. .*.**.*.....***.**.*.. *..*.*........*.*.*... **.................... Still lifes have been enumerated by Conway (4-7 bits), Robert Wainwright (8-10 bits), Dave Buckingham (11-13 bits), Peter Raynham (14 bits) and Mark Niemiec (15-24 bits). The resulting figures are shown below. (These figures shouldn't be affected by the above discussion of the strict definition of "still life", because it is unlikely that there are any doubtful cases with much less than 32 cells.) ------------- Bits Number ------------- 4 2 5 1 6 5 7 4 8 9 9 10 10 25 11 46 12 121 13 240 14 619 15 1353 16 3286 17 7773 18 19044 19 45759 20 112243 21 273188 22 672172 23 1646147 24 4051711 ------------- :still life tagalong: A {tagalong} which takes the form of a {still life} in at least one {phase}. An example is shown below. ..**............... .**.**............. ..****............. ...**.............. ................... ...*****........... ..*******.......... .**.*****.......... ..**............... ................... ........*.*.....**. ......*....*...*..* ......**.....*.*..* .*..*..****.*...**. *.......**......... *...*.............. ****............... :stretcher: Any pattern that grows by stretching a {wick} or {agar}. See {wickstretcher} and {spacefiller}. :strict volatility: A term suggested by Noam Elkies in August 1998 for the proportion of cells involved in a period n {oscillator} which themselves oscillate with period n. For prime n this is the same as the ordinary {volatility}. :super beehive: = {honeycomb} :superfountain: (p4) A p4 {sparker} which produces a 1-cell spark that is separated from the rest of the oscillator by two clear rows of cells. The first superfountain was found by Noam Elkies in February 1998. In January 2006 Nicolay Beluchenko found the much smaller one shown below. See also {fountain}. ...........*........... ....................... ....................... .....*..*.....*..*..... ...**..*.*****.*..**... .....*...........*..... ...*.**.........**.*... .*.*...***...***...*.*. ***.*.............*.*** ..........*.*.......... ....***...*.*...***.... ....*..*...*...*..*.... ...****..*.*.*..****... ...**..***.*.***..**... ..*...*...*.*...*...*.. ...*..*.*.*.*.*.*..*... ....*.*.**...**.*.*.... .....*...........*..... :superstring: An infinite orthogonal row of cells stabilized on one side so that it moves at the {speed of light}, often leaving debris behind. The first examples were found in 1971 by Edward Fitzgerald and Robert Wainwright. Superstrings were studied extensively by Peter Rott during 1992-1994, and he found examples with many different periods. (But no odd periods. In August 1998 Stephen Silver proved that odd-period superstrings are impossible.) Sometimes a finite section of a superstring can be made to run between two tracks ("waveguides"). This gives a {fuse} which can be made as wide as desired. The first example was found by Tony Smithurst and uses {tub}s. (This is shown below. The superstring itself is p4 with a repeating section of width 9 producing one blinker per period and was one of those discovered in 1971. With the track in place, however, the period is 8. This track can also be used with a number of other superstrings.) Shortly after seeing this example, in March 1997 Peter Rott found another superstring track consisting of {boat}s. At present these are the only two waveguides known. Both are destroyed by the superstring as it moves along - it would be interesting to find one that remains intact. See {titanic toroidal traveler} for another example of a superstring. .**.......................................................... *..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*. ....*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.* *..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*. .***......................................................... ..**......................................................... ..**......................................................... ...*......................................................... ...*......................................................... ...*......................................................... ...*......................................................... ...*......................................................... ...*......................................................... ...*......................................................... ..**......................................................... ..**......................................................... .***......................................................... *..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*. ....*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.* *..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*. .**.......................................................... :support: Those parts of an object which are only present in order to keep the rest of the object (such an {engine} or an edge {spark}) working correctly. These can be components of the object, or else accompanying objects used to {perturb} the object. In many cases there is a wide variation of support possible for an engine. The {arm}s in many {puffer}s are an example of support. :surprise: (p3) Found by Dave Buckingham, November 1972. ...*....** ...***..*. .**...*.*. *..**.*.** .*......*. **.*.**..* .*.*...**. .*..***... **....*... :swan: (c/4 diagonally, p4) A diagonal {spaceship} producing some useful sparks. Found by Tim Coe in February 1996. .*..........**.......... *****......**........... *..**........*.......**. ..**.*.....**......***.* ...........**...*.**.... .....*.*......**........ ..........***.*....*.... .......***...*....*..... ........*.......*....... ........*......*........ ........................ ...........*............ :switch engine: The following pattern, which in itself is unstable, but which can be used to make c/12 diagonal {puffer}s and {spaceship}s. .*.*.. *..... .*..*. ...*** The switch engine was discovered by Charles Corderman in 1971. He also found the two basic types of stabilized switch engine: a p288 block-laying type (the more common of the two) and p384 glider-producing type. These two puffers are the most {natural} infinite growth patterns in Life, being the only ones ever seen to occur from random starting patterns. Patterns giving rise to block-laying switch engines can be seen under {infinite growth}, and one giving rise to a glider-producing switch engine is shown under {time bomb}. See also {Cordership} and {ark}. :synthesis: = {glider synthesis} :T: = {T-tetromino} :table: The following {induction coil}. **** *..* :table on table: (p1) *..* **** .... **** *..* :tag: = {tagalong} :tagalong: An object which is not a {spaceship} in its own right, but which can be attached to one or more spaceships to form a larger spaceship. For examples see {Canada goose}, {fly}, {pushalong}, {sidecar} and {sparky}. See also {Schick engine}, which consists of a tagalong attached to two LWSS (or similar). :tail spark: A {spark} at the back of a spaceship. For example, the 1-bit spark at the back of a {LWSS}, {MWSS} or {HWSS} in their less dense phases. :tame: To {perturb} a {dirty} reaction using other patterns so as to make it {clean} and hopefully useful. Or to make a reaction work which would otherwise fail due to unwanted products which interfere with the reaction. :taming: See {tame}. :teardrop: The following {induction coil}, or the formation of two beehives that it evolves into after 20 generations. (Compare {butterfly}, where the beehives are five cells further apart.) ***. *..* *..* .**. :technician: (p5) Found by Dave Buckingham, January 1973. .....*..... ....*.*.... ....**..... ..**....... .*...***... *..**...*.* .**....*.** ...*.*.*... ...*...*... ....***.... ......*.*.. .......**.. :technician finished product: = {technician} :teeth: A 65-cell quadratic growth pattern found by Nick Gotts in March 2000. This (and a related 65-cell pattern which Gotts found at about the same time) beat the record previously held by {mosquito5} for smallest population known to have superlinear growth. Now superseded by {catacryst} and {metacatacryst}. :ternary reaction: Any reaction between three objects. In particular, a reaction in which two gliders from one stream and one glider from a crossing stream of the same period annihilate each other. This can be used to combine two glider guns of the same period to produce a new glider gun with double the period. :test tube baby: (p2) **....** *.*..*.* ..*..*.. ..*..*.. ...**... :tetraplet: Any 4-cell {polyplet}. :tetromino: Any 4-cell {polyomino}. There are five such objects, shown below. The first is the {block}, the second is the {T-tetromino} and the remaining three rapidly evolve into {beehive}s. **......***......****......***......**. **.......*...................*.......** :The Recursive Universe: A popular science book by William Poundstone (1985) dealing with the nature of the universe, illuminated by parallels with the game of Life. This book brought to a wider audience many of the results that first appeared in {LifeLine}. It also outlines the proof of the existence of a {universal constructor} in Life first given in {Winning Ways}. :thumb: A {spark}-like protrusion which flicks out in a manner resembling a thumb being flicked. Here are two examples. On the left is a p9 thumb sparker found by Dean Hickerson in October 1998. On the right is a p4 one found by David Eppstein in June 2000. .......*..............*..... ...**...*.........**...*.... ...*.....*.**.....*.....*... **.*.*......*......***.*.**. **.*.**.****............**.* ...*.*...........******....* ...*.*.***.......*....*****. ....*.*...*.........*....... ......*..**........*.****... ......**...........*.*..*... ....................*....... :thunderbird: (stabilizes at time 243) *** ... .*. .*. .*. :tick: = {generation} :tie: A term used in naming certain {still life}s (and the {stator} part of certain {oscillator}s). It indicates that the object consists of two smaller objects joined point to point, as in {ship tie boat}. :time bomb: The following pattern by Doug Petrie, which is really just a glider-producing {switch engine} in disguise. See {infinite growth} for some better examples of a similar nature. .*...........** *.*....*......* .......*....*.. ..*..*...*..*.. ..**......*.... ...*........... :titanic toroidal traveler: The {superstring} with the following repeating segment. The front part becomes p16, but the eventual fate of the detached back part is unknown. ****** ***... :TL: = {traffic light} :T-nosed p4: (p4) Found by Robert Wainwright in October 1989. See also {filter}. .....*..... .....*..... ....***.... ........... ........... ........... ...*****... ..*.***.*.. ..*.*.*.*.. .**.*.*.**. *..**.**..* **.......** :T-nosed p6: (p6) Found by Achim Flammenkamp in September 1994. There is also a much larger and fully symmetric version found by Flammenkamp in August 1994. ......**...**...... ......*.*.*.*...... .......*...*....... ................... ..*.*.*.....*.*.*.. ***.*.**...**.*.*** ..*.*.*.....*.*.*.. ................... .......*...*....... ......*.*.*.*...... ......**...**...... :toad: (p2) Found by Simon Norton, May 1970. This is the second most common {oscillator}, although {blinker}s are more than a hundred times as frequent. See also {killer toads}. .*** ***. :toad-flipper: A {toad} {hassler} that works in the manner of the following example. Two {domino} {sparker}s, here {pentadecathlon}s, apply their {spark}s to the toad in order to flip it over. When the sparks are applied again it is flipped back. Either or both domino sparkers can be moved down two spaces from the position shown and the toad-flipper will still work, but because of symmetry there are really only two different types. Compare {toad-sucker}. .*..............*. .*..............*. *.*............*.* .*..............*. .*......*.......*. .*......**......*. .*......**......*. *.*......*.....*.* .*..............*. .*..............*. :toad-sucker: A {toad} {hassler} that works in the manner of the following example. Two {domino} {sparker}s, here {pentadecathlon}s, apply their {spark}s to the toad in order to shift it. When the sparks are applied again it is shifted back. Either or both domino sparkers can be moved down two spaces from the position shown and the toad-sucker will still work, but because of symmetry there are really only three different types. Compare {toad-flipper}. .*................ .*..............*. *.*.............*. .*.............*.* .*......*.......*. .*......**......*. .*......**......*. *.*......*......*. .*.............*.* .*..............*. ................*. :toaster: (p5) Found by Dean Hickerson, April 1992. ....*......**.. ...*.*.**..*... ...*.*.*.*.*... ..**.*...*.**.. *...**.*.**...* ...*.......*... ...*.......*... *...**.*.**...* ..**.*...*.**.. ...*.*.*.*.*... ...*.*.**..*... ....*......**.. :torus: As applies to Life, usually means a finite Life universe which takes the form of an m x n rectangle with the bottom edge considered to be joined to the top edge and the left edge joined to the right edge, so that the universe is topologically a torus. There are also other less obvious ways of obtaining an toroidal universe. See also {Klein bottle}. :total aperiodic: Any finite pattern which evolves in such a way that no cell in the Life plane is eventually periodic. The first example was found by Bill Gosper in November 1997. A few days later he found the following much smaller example consisting of three copies of a p12 {backrake} by Dave Buckingham. .........................................*................. ........................................***................ .......................................**.*.....*.......... .......................................***.....***......... ........................................**....*..**...***.. ..............................................***....*..*.. ........................................................*.. ........................................................*.. ........................................................*.. ........................................***............*... ........................................*..*............... ........................................*.................. ........................................*.................. .........................................*................. ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ......................................***.................. ......................................*..*...........*..... ......................................*.............***.... ......................................*............**.*.... ......................................*............***..... .......................................*............**..... ........................................................... ........................................................... ...................................***..................... ..................................*****.................... ..................................***.**.......**........*. .....................................**.......****........* ..............................................**.**...*...* ................................................**.....**** ........................................................... ........................................................... ....................*...................................... .....................*..................................... .**.............*....*................................***.. ****.............*****..................................*.. **.**...................................................*.. ..**...................................................*... ....................................*...................... .....................................*..................... .....................**..........*...*..................... ......................**..........****...............**.... .....................**...........................***.**... .....................*............................*****.... ...................................................***..... ........................................................... ......................**................................... .............****....****.................................. ............*...*....**.**................................. .*****..........*......**.................................. *....*.........*........................................... .....*..................................................... ....*...................................................... :T-pentomino: Conway's name for the following {pentomino}, which is a common {parent} of the {T-tetromino}. *** .*. .*. :track: A path made out of {conduit}s, often ending where it begins so that the active object is cycled forever, forming an {oscillator} or a {gun}. :tractor beam: A stream of {spaceship}s that can draw an object towards the source of the stream. The example below shows a tractor beam pulling a {loaf}; this was used by Dean Hickerson to construct a {sawtooth}. .....................*..*...................... .....****...........*..............****........ .....*...*..........*...*..........*...*....... .....*........**....****...........*........**. .**...*..*...****...........**......*..*...**** *..*........**.**..........**.**..........**.** *.*..........**.............****...........**.. .*...........................**................ :traffic circle: (p100) .....................**....**................... .....................*.*..*.*................... .......................*..*..................... ......................**..**.................... .....................***..***................... .......................*..*..................... ...............................*................ ..............................*.**.............. ..................................*............. ..........................*...*..*.*............ ..........................*.....*..*............ ..........................*......**............. .........**..................................... ........*..*..........***...***................. .......*.*.*.................................... ......***.*...............*..................... ......***.................*..................... ..........................*..................... ............***................................. **..*................***........................ *..**.....*.....*............................... .*****....*.....*..*.....*.................*..** ..........*.....*..*.....*.................**..* ...................*.....*.......***......*****. .*****......***................................. *..**................***.......*.....*.......... **..*..........................*.....*....*****. ...............................*.....*.....**..* ...........................................*..** .................................***............ .......................................**....... ......................................***....... .....................................*.**....... ....................................*.*......... ....................***.............*..*........ .....................................**......... .............**....*..*......................... ............*..*................................ ............*.*.*............................... .............*..*............................... .................*.............................. ..............*.*............................... .....................*..*....................... ...................***..***..................... ....................**..**...................... .....................*..*....................... ...................*.*..*.*..................... ...................**....**..................... :traffic jam: Any {traffic light} {hassler}, such as {traffic circle}. The term is also applied to the following reaction, used in most traffic light hasslers, in which two traffic lights interact in such a way as to reappear after 25 generations with an extra 6 spaces between them. ..***........... ...........***.. *.....*......... *.....*..*.....* *.....*..*.....* .........*.....* ..***........... ...........***.. :traffic light: (p2) A common formation of four blinkers. ..***.. ....... *.....* *.....* *.....* ....... ..***.. :trans-beacon on table: (p2) ....** .....* ..*... ..**.. ...... ****.. *..*.. :trans-boat with tail: (p1) **... *.*.. .*.*. ...*. ...** :transceiver: See {Herschel transceiver}. :trans-loaf with tail: (p1) .*.... *.*... *..*.. .**.*. ....*. ....** :transmitter: See {Herschel transmitter}. :transparent block reaction: A certain reaction between a block and a {Herschel} {predecessor} in which the block reappears in its original place some time later, the reaction having effectively passed through it. This reaction was found by Dave Buckingham in 1988. It has been used in some {Herschel conduit}s, and in the {gunstar}s. Because the reaction involves a Herschel predecessor rather than an actual Herschel, the following diagram shows instead a {B-heptomino} (which by itself would evolve into a block and a Herschel). *............. **..........** .**.........** **............ :transparent debris effect: A reaction in which a {Herschel} or other active region destroys a {still life}, then later, having passed through the place where the still life was, recreates the still life in its original position. For an example, see {transparent block reaction}. :trice tongs: (p3) Found by Robert Wainwright, February 1982. In terms of its 7x7 {bounding box} this ties with {jam} as the smallest p3 {oscillator}. ..*.... ..***.. **...*. .*.*.*. .*..... ..**..* .....** :triomino: Either of the two 3-cell {polyomino}es. The term is rarely used in Life, since the two objects in question are simply the {blinker} and the {pre-block}. :triple caterer: (p3) Found by Dean Hickerson, October 1989. Compare {caterer} and {double caterer}. .....**......... ....*..*..**.... ....**.*...*.... ......*.***....* ..***.*.*....*** .*..*..*....*... *.*..*...*..**.. .*.............. ..**.**.**.**... ...*...*...*.... ...*...*...*.... :triplet: Any 3-cell {polyplet}. There are 5 such objects, shown below. The first two are the two {triomino}es, and the other three vanish in two generations. *..................*.......*.......*.. **......***......**.......*.*.......*. .....................................* :tripole: (p2) The {barberpole} of length 3. **.... *.*... ...... ..*.*. .....* ....** :tritoad: (p3) Found by Dave Buckingham, October 1977. .........**....... .........*........ ..........*..**... .......***.*..*... ......*....**.*.** ......*.**..*.*.** ...**.*...**..*... ...*..**...*.**... **.*.*..**.*...... **.*.**....*...... ...*..*.***....... ...**..*.......... ........*......... .......**......... :true: Opposite of {pseudo}. A {gun} emitting a period n stream of {spaceship}s (or {rake}s) is said to be a true period n gun if its mechanism oscillates with period n. (The same distinction between true and pseudo also exists for {puffer}s.) True period n guns are known to exist for all periods greater than 61 (see {My Experience with B-heptominos in Oscillators}), but only a few smaller periods have been achieved, namely 22, 24, 30, 36, 44, 46, 48, 50, 54, 55, 56 and 60. (Credits for these small period guns are: p30, p46 and p60 by Bill Gosper in 1970-1971, p44 by Dave Buckingham in 1992, p50 by Dean Hickerson in 1996, p24 and p48 by Noam Elkies in 1997, p54 and p56 by Dieter Leithner in early 1998, p55 by Stephen Silver in late 1998, p22 by David Eppstein in 2000 and p36 by Jason Summers in 2004.) The following diagram shows the p22 gun (David Eppstein, August 2000, using two copies of a p22 oscillator found earlier the same day by Jason Summers). ..................**......................... ...................*.......*................. ...................*.*..............**....... ....................**............**..*...... ........................***.......**.**...... ........................**.**.......***...... ........................*..**............**.. .........................**..............*.*. ...................................*.......*. ...........................................** ............................................. **.......................*................... .*.....................*.*................... .*.*.............***....**................... ..**...*........*...*........................ ......*.**......*....*....................... .....*....*......**.*.........*.............. ......*...*........*...**......*............. .......***.............*.*...***............. .........................*................... .........................**.................. :T-tetromino: The following common {predecessor} of a {traffic light}. *** .*. :tub: (p1) .*. *.* .*. :tubber: (p3) Found by Robert Wainwright before June 1972. ....*.*...... ....**.*..... .......***... ....**....*.. **.*..**..*.. .*.*....*.**. *...*...*...* .**.*....*.*. ..*..**..*.** ..*....**.... ...***....... .....*.**.... ......*.*.... :tubeater: A pattern that consumes the output of a {tubstretcher}. The smallest known tubeater was found by Hartmut Holzwart, and is shown below in conjunction with the smallest known tubstretcher. .......**......................... .......*.*........................ .......*.......................... ..........*....................... ..........**...................... ..........**...................... .........**....................... **......**...*.................... *.*...**..*.*.*................... *.....***....*.*.................. ...*..........*.*................. ...**..........*.*................ ................*.*............... .................*.*...*.......... ..................**..*.*......... .....................**.*......... .....................**........... .....................**........... ...............................**. .......................*....**.*.. .......................***..**.... .......................***..**.... ........................**........ .................................. ..........................*....... .........................**....... .........................*........ ..........................*....... .................................. ...........................**..... ............................*.**.. ................................*. .............................**... .............................**... ...............................*.. ................................** :tubstretcher: Any {wickstretcher} in which the wick is two diagonal lines of cells forming, successively, a {tub}, a {barge}, a {long barge}, etc. The first one was found by Hartmut Holzwart in June 1993, although at the time this was considered to be a boatstretcher (as it was shown with an extra cell, making the tub into a {boat}). The following small example is by Nicolay Beluchenko (August 2005), using a {quarter}. .......***..... .......*....... ........*...... ..........**... ...........*... ............... ........**...*. ***.....**..*.* *......*.*...*. .*....**....... ...****.*...... ....**......... :tub with tail: (p1) .*... *.*.. .*.*. ...*. ...** :tugalong: = {tagalong} :tumbler: (p14) The smallest known p14 {oscillator}. Found by George Collins in 1970. .*.....*. *.*...*.* *..*.*..* ..*...*.. ..**.**.. :tumbling T-tetson: (p8) A {T-tetromino} {hassle}d by two {figure-8}s. Found by Robert Wainwright. .***................. *..................** *...*............*.** *..*.*..........*.... ..*.*..*...........*. ...*...*.......**.*.. .......*.......**.... ....***....*......... .........**.......... ...........*......... :Turing machine: See {universal computer}. :turning toads: (p4 wick) Found by Dean Hickerson, October 1989. ..............**.....**.....**.....**.....**.............. .......*.....*......*......*......*......*................ ......**...*....*.*....*.*....*.*....*.*....*.*.*.**...... ..**.*.***.*..**..*..**..*..**..*..**..*..**..*..*..*.**.. *..*.**.........................................*****.*..* **.*..............................................**..*.** ...*..................................................*... ...**................................................**... :turtle: (c/3 orthogonally, p3) Found by Dean Hickerson. .***.......* .**..*.**.** ...***....*. .*..*.*...*. *....*....*. *....*....*. .*..*.*...*. ...***....*. .**..*.**.** .***.......* :twin bees shuttle: (p46) Found by Bill Gosper in 1971, this is the basis of all known p46 oscillators, and so of all known {true} p46 {gun}s (see {new gun} for an example). There are numerous ways to stabilize the ends, two of which are shown in the diagram. On the left is David Bell's {double block reaction} (which results in a shorter, but wider, shuttle than usual), and on the right is the stabilization by a single block. This latter method produces a very large {spark} which is useful in a number of ways (see, for example, {metamorphosis}). Adding a symmetrically placed block below this one suppresses the spark. See also {p54 shuttle}. .**........................ .**........................ ........................... ...............*........... **.............**........** **..............**.......** ...........**..**.......... ........................... ........................... ........................... ...........**..**.......... **..............**......... **.............**.......... ...............*........... ........................... .**........................ .**........................ :twinhat: (p1) See also {hat} and {sesquihat}. ..*...*.. .*.*.*.*. .*.*.*.*. **.*.*.** ....*.... :twin peaks: = {twinhat} :twirling T-tetsons II: (p60) Found by Robert Wainwright. This is a {pre-pulsar} {hassle}d by {killer toads}. .......**...**.......... ......*.......*......... .........*.*............ .......**...**.......... ........................ ........................ ........................ .....................*** ....................***. .............*.......... ***.........***......... .***.................... ....................***. .....................*** ........................ .***.................... ***.........***......... .............*.......... ........................ ........................ ..........**...**....... ............*.*......... .........*.......*...... ..........**...**....... :TWIT: = {tub with tail} :two eaters: (p3) Found by Bill Gosper, September 1971. **....... .*....... .*.*..... ..**..... .....**.. .....*.*. .......*. .......** :two pulsar quadrants: (p3) Found by Dave Buckingham, July 1973. Compare {pulsar quadrant}. ....*.... ....*.... ...**.... ..*...... *..*..*** *...*.*.. *....*... ......... ..***.... :underpopulation: Death of a cell caused by it having fewer than two {neighbour}s. See also {overpopulation}. :unit Life cell: A rectangular pattern, of size greater than 1x1, that can simulate Life in the following sense. The pattern by itself represents a dead Life cell, and some other pattern represents a live Life cell. When the plane is tiled by these two patterns (which then represent the state of a whole Life universe) they evolve, after a fixed amount of time, into another tiling of the plane by the same two patterns which correctly represents the Life generation following the one they initially represented. It is usual to use capital letters for the simulated things, so, for example, for the first known unit Life cell (constructed by David Bell in January 1996), one Generation is 5760 generations, and one Cell is 500x500 cells. In December 2005, Jason Summers constructed an analogous unit cell for Wolfram's Rule 100, a one-dimensional {cellular automaton} that is know be universal. :universal computer: A computer that can compute anything that is computable. (The concept of computability can be defined in terms of Turing machines, or by Church's lambda calculus, or by a number of other methods, all of which can be shown to lead to equivalent definitions.) The relevance of this to Life is that both Bill Gosper and John Conway proved early on that it is possible to construct a universal computer in the Life universe. (To prove the universality of a {cellular automaton} with simple rules was in fact Conway's aim in Life right from the start.) Conway's proof is outlined in {Winning Ways}, and also in {The Recursive Universe}. Until recently, no universal Life computer had ever been built in practice, because it would be enormous, even with the improvements that have been devised since those early proofs. In April 2000, Paul Rendell completed a Turing machine construction (described in {http://www.cs.ualberta.ca/~bulitko/F02/papers/tm_words.pdf}). This, however, has a finite tape, as opposed to the infinite tape of a true Turing machine, and is therefore not a universal computer. But in November 2002, Paul Chapman announced the construction of a universal computer, details of which can be found at {http://www.igblan.free-online.co.uk/igblan/ca/}. This is a universal register machine based around Dean Hickerson's {sliding block memory}. See also {universal constructor}. :universal constructor: A pattern that is capable of constructing almost any pattern that has a {glider synthesis}. This definition is a bit vague. A precise definition seems impossible because it has not been proved that all possible glider fleets are constructible. In any case, a universal constructor ought to be able to construct itself in order to qualify as such. An outline of Conway's proof that such a pattern exists can be found in {Winning Ways}, and also in {The Recursive Universe}. The key mechanism for the production of gliders with any given path and timing is known as side-tracking, and is based on the {kickback reaction}. A universal constructor designed in this way can also function as a universal destructor - it can delete almost any pattern that can be deleted by gliders. In May 2004, Paul Chapman and Dave Greene produced a prototype programmable universal constructor. This is able to construct objects by means of {slow glider construction}s. It likely that it could be programmed to be construct itself, but the necessary program would be very large; moreover an additional mechanism would be needed in order to copy the program. A universal constructor is most useful when attached to a {universal computer}, which can be programmed to control the constructor to produce the desired pattern of gliders. In what follows I will assume that a universal constructor always includes this computer. The existence of a universal constructor/destructor has a number of theoretical consequences. For example, the constructor could be programmed to make copies of itself. This is a {replicator}. The constructor could even be programmed to make just one copy of itself translated by a certain amount and then delete itself. This would be a (very large, very high period) {spaceship}. Any translation is possible (except that it must not be too small), so that the spaceship could travel in any direction. It could also travel slower than any given speed, since we could program it to perform some time-wasting task (such as repeatedly constructing and deleting a block) before copying itself. Of course, we could also choose for it to leave some debris behind, thus making a {puffer}. It is also possible to show that the existence of a universal constructor implies the existence of a {stable} {reflector}. This proof is not so easy, however, and is no longer of much significance now that explicit examples of such reflectors are known. :universal destructor: See {universal constructor}. :universal register machine: = {URM} :universal regulator: A {regulator} in which the incoming gliders are aligned to period 1, that is, they have arbitrary timing (subject to some minimum time required for the regulator to recover from the previous glider). Paul Chapman constructed the first universal regulator in March 2003. It is adjustable, so that the output can be aligned to any desired period. :unix: (p6) Two {block}s eating a {long barge}. This is a useful {sparker}, found by Dave Buckingham in February 1976. The name derives from the fact that it was for some time the mascot of the Unix lab of the mathematics faculty at the University of Waterloo. .**..... .**..... ........ .*...... *.*..... *..*..** ....*.** ..**.... :up boat with tail: = {trans-boat with tail} :U-pentomino: Conway's name for the following {pentomino}, which rapidly dies. *.* *** :URM: A universal register machine, particularly Paul Chapman's Life implementation of such a machine. See {universal computer} for more information. :vacuum: Empty space. That is, space containing only dead {cell}s. :Venetian blinds: The p2 {agar} obtained by using the pattern O..O to tile the plane. :very long: = {long long} :very long house: The following {induction coil}. .*****. *..*..* **...** :volatility: The volatility of an {oscillator} is the size (in cells) of its {rotor} divided by the sum of the sizes of its rotor and its {stator}. In other words, it is the proportion of cells involved in the oscillator which actually oscillate. For many periods there are known oscillators with volatility 1, see for example {Achim's p16}, {figure-8}, {Kok's galaxy}, {mazing}, {pentadecathlon}, {phoenix}, {relay}, {smiley} and {tumbler}. The smallest period for which the existence of such statorless oscillators is undecided is 3, although Dean Hickerson showed in 1994 that there are p3 oscillators with volatility arbitrarily close to 1 (as is the case for all but finitely many periods, because of the possibility of feeding the gliders from a {true} period n {gun} into an {eater}). The term "volatility" is due to Robert Wainwright. See also {strict volatility}. :volcano: Any of a number of p5 oscillators which produce sparks. See {lightweight volcano}, {middleweight volcano} and {heavyweight volcano}. :V-pentomino: Conway's name for the following {pentomino}, a {loaf} {predecessor}. *.. *.. *** :washerwoman: (2c/3 p18 fuse) A {fuse} by Earl Abbe. *....................................................... **....*.....*.....*.....*.....*.....*.....*.....*.....*. ***..*.*...*.*...*.*...*.*...*.*...*.*...*.*...*.*...*.* **....*.....*.....*.....*.....*.....*.....*.....*.....*. *....................................................... :washing machine: (p2) Found by Robert Wainwright before June 1972. .**.**. *.**..* **....* .*...*. *....** *..**.* .**.**. :wasp: (c/3 orthogonally, p3) The following {spaceship} which produces a {domino} {spark} at the back. It is useful for {perturb}ing other objects. Found by David Bell, March 1998. ..........**.**....... ........**.*.**.**.... .....***.*..***..****. .***....***.....*....* *.*.*.***.*........**. *.*.*.****............ .*.*....*..*.......... ..........*........... ..*................... ..*................... :wavefront: (p4) Found by Dave Buckingham, 1976 or earlier. ........**... ........*.... .........*... ........**... .....**...**. ....*..***..* ....*.....**. .....*...*... **.*.*...*... *.**.*.**.... ....*.*...... ....*.*...... .....*....... :waveguide: See {superstring}. :weekender: (2c/7 orthogonally, p7) Found by David Eppstein in January 2000. In April 2000 Stephen Silver found a tagalong for a pair of weekenders. At present, n weekenders pulling n-1 tagalongs constitute the only known {spaceship}s of this speed or period. .*............*. .*............*. *.*..........*.* .*............*. .*............*. ..*...****...*.. ......****...... ..****....****.. ................ ....*......*.... .....**..**..... :weld: To join two or more {still life}s or {oscillator}s together. This is often done in order to fit the objects into a smaller space than would otherwise be possible. The simplest useful example is probably the {integral sign}, which can be considered as a pair of welded {eater1}s. :Wheels, Life, and other Mathematical Amusements: One of Martin Gardner's books (1983) that collects together material from his column in Scientific American. The last three chapters of this book contain all the Life stuff. :why not: (p2) Found by Dave Buckingham, July 1977. ...*... ...*.*. .*..... *.***** .*..... ...*.*. ...*... :wick: A stable or oscillating linearly repeating pattern that can be made to burn at one end. See {fuse}. :wickstretcher: A {spaceship}-like object which stretches a {wick} that is fixed at the other end. The wick here is assumed to be in some sense connected, otherwise most {puffer}s would qualify as wickstretchers. The first example of a wickstretcher was found in October 1992 (front end by Hartmut Holzwart and back end by Dean Hickerson) and stretches {ants} at a speed of c/4. This is shown below with an improved back end found by Hickerson the following month. .................**.............................. .............**....*............................. ............***.*................................ *.**..**...*...****.*.*....**.......**........... *....**..*........*.***....*....**.*..*.**.*..... *.**....**.**....*...........*...*.*.**.*.**..... ......*.......*.............**.....*..*.*...**... .....*.........*.*....***...*....*..*.*.***...*.. .....*.........*.*....***.**.*..**.*.*...*..**.*. ......*.......*.............**.*...**....**....*. *.**....**.**....*..........*........**.*.*.**.** *....**..*........*.***........*...*...**.*..*.*. *.**..**...*...****.*.*.......*.*...**....*..*.*. ............***.*..............*.....*.***....*.. .............**....*.................*.*......... .................**...................*.......... Diagonally moving c/4 and c/12 wickstretchers have also been built: see {tubstretcher} and {linestretcher}. In July 2000 Jason Summers constructed a c/2 wickstretcher, stretching a p50 {traffic jam} wick, based on an earlier (October 1994) pattern by Hickerson. :wicktrailer: Any {extensible} {tagalong}, that is, one which can be attached to the back of itself, as well as to the back of a {spaceship}. The number of generations which it takes for the tagalong to occur again in the same place is often called the period of the wicktrailer - this has little relation to the period of the tagalong units themselves. :windmill: (p4) Found by Dean Hickerson, November 1989. ...........*...... .........**.*..... .......**......... ..........**...... .......***........ .................. ***............... ...**..***.**..... ..........*******. .*******.......... .....**.***..**... ...............*** .................. ........***....... ......**.......... .........**....... .....*.**......... ......*........... :wing: The following {induction coil}. This is generation 2 of {block and glider}. .**. *..* .*.* ..** :WinLifeSearch: Jason Summers' GUI version of {lifesrc} for MS Windows. It is available from {http://entropymine.com/jason/life/software/}. :Winning Ways: A two-volume book (1982) by Elwyn Berlekamp, John Conway and Richard Guy on mathematical games. The last chapter of the second volume concerns Life, and outlines a proof of the existence of a {universal constructor}. :with-the-grain grey ship: A {grey ship} in which the region of density 1/2 consists of lines of ON cells lying parallel to the direction in which the spaceship moves. See also {against-the-grain grey ship}. :WLS: = {WinLifeSearch} :worker bee: (p9) Found by Dave Buckingham in 1972. Unlike the similar {snacker} this produces no {spark}s, and so is not very important. Like the snacker, the worker bee is {extensible} - it is, in fact, a finite version of the infinite oscillator which consists of six ON cells and two OFF cells alternating along a line. Note that Dean Hickerson's new snacker ends also work here. **............** .*............*. .*.*........*.*. ..**........**.. ................ .....******..... ................ ..**........**.. .*.*........*.*. .*............*. **............** :W-pentomino: Conway's name for the following {pentomino}, a common {loaf} {predecessor}. *.. **. .** :x66: (c/2 orthogonally, p4) Found by Hartmut Holzwart, July 1992. Half of this can be escorted by a HWSS. The name refers to the fact that every cell (live or dead) has at most 6 live neighbours (in contrast to {spaceship}s based on {LWSS}, {MWSS} or {HWSS}). In fact this spaceship was found by a search with this restriction. ..*...... **....... *..***..* *....***. .***..**. ......... .***..**. *....***. *..***..* **....... ..*...... :Xlife: A popular freeware Life program that runs under the X Window System. The main Life code was written by Jon Bennett, and the X code by Chuck Silvers. :X-pentomino: Conway's name for the following {pentomino}, a {traffic light} {predecessor}. .*. *** .*. :Y-pentomino: Conway's name for the following {pentomino}, which rapidly dies. ..*. **** :Z-hexomino: The following {hexomino}. The Z-hexomino features in the {pentoad}, and also in {Achim's p144}. **. .*. .*. .** :Z-pentomino: Conway's name for the following {pentomino}, which rapidly dies. **. .*. .** :zweiback: (p30) An oscillator in which two {HW volcano}es {hassle} a {loaf}. This was found by Mark Niemiec in February 1995 and is too big to show here. ----------------------------------------------------------------------- Bibliography. David I. Bell, "Spaceships in Conway's Life". Series of articles posted on comp.theory.cell-automata, Aug-Oct 1992. Now available from his web-site (http://www.canb.auug.org.au/~dbell/). David I. Bell, "Speed c/3 Technology in Conway's Life", 17 December 1999. Available from his web-site (see above). Elwyn R. Berlekamp, John H. Conway and Richard K. Guy, "Winning Ways for your Mathematical Plays, II: Games in Particular". Academic Press, 1982. David J Buckingham, "Some Facts of Life". BYTE, December 1978. Dave Buckingham, "My Experience with B-heptominos in Oscillators". 12 October 1996. Available from Paul Callahan's web-site (http://www.radicaleye.com/lifepage/patterns/bhept/bhept.html). David J. Buckingham and Paul B. Callahan, "Tight Bounds on Periodic Cell Configurations in Life". Experimental Mathematics 7:3 (1998) 221-241. Available at http://www.expmath.org/restricted/7/7.3/callahan.ps.gz . Noam D. Elkies, "The still-Life density problem and its generalizations", pp228-253 of "Voronoi's Impact on Modern Science, Book I", P. Engel, H. Syta (eds), Institute of Mathematics, Kyiv 1998 = Vol.21 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine, math.CO/9905194 (http://front.math.ucdavis.edu/math.CO/9905194). Martin Gardner, "Wheels, Life, and other Mathematical Amusements". W. H. Freeman and Company, 1983. R. Wm. Gosper, "Exploiting Regularities in Large Cellular Spaces". Physica 10D (1984) 75-80. N. M. Gotts and P. B. Callahan, "Emergent structures in sparse fields of Conway's 'Game of Life'", in "Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life", MIT Press, 1998. Mark D Niemiec, "Life Algorithms". BYTE, January 1979. William Poundstone, "The Recursive Universe". William Morrow and Company Inc., 1985.