eternity_tile
eternity_tile,
an Octave code which
considers the individual tiles of the eternity puzzle,
209 distinct pieces, each formed by 36
contiguous 30-60-90 triangles, known as polydrafters,
as well as tiles for the serenity and trinity puzzles,
and the hat and turtle aperiodic monotile.
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
eternity_tile is available in
a MATLAB version and
an Octave version.
Related Data and Programs:
eternity_tile_test
eternity,
an Octave code which
considers the eternity puzzle, which considers an irregular dodecagon
shape that is to be tiled by 209 distinct pieces, each formed by 36
contiguous 30-60-90 triangles, known as polydrafters.
pariomino,
an Octave code which
considers pariominoes, which are polyominoes with a checkerboard parity,
and the determination of tilings of a region using a specific set of
pariominoes.
polyiamonds,
an Octave code which
considers polyiamonds, simple connected shapes constructed from
equilateral triangles connected edgewise.
polyominoes,
an Octave code which
defines, solves, and plots a variety of polyomino tiling problems,
which are solved by a direct algebraic approach involving the
reduced row echelon form (RREF) of a specific matrix, instead of the
more typical brute-force or backtracking methods.
trinity,
an Octave code which
considers the trinity puzzle, a smaller version of the eternity
puzzle. The trinity puzzle specifies a region R composed of 144
30-60-90 triangles, and a set of 4 "tiles", T1, T2, T3 and T4,
each consisting of 36 30-60-90 triangles, and seeks an arrangement
of the four tiles that exactly covers the region.
Reference:
-
Marcus Garvie, John Burkardt,
A new mathematical model for tiling finite regions of the plane
with polyominoes,
Contributions to Discrete Mathematics,
Volume 15, Number 2, July 2020.
-
Solomon Golomb,
Polyominoes: Puzzles, Patterns, Problems, and Packings,
Princeton University Press, 1996,
ISBN: 9780691024448
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Ed Pegg,
Polyform Patterns,
in Tribute to a Mathemagician,
Barry Cipra, Erik Demaine, Martin Demaine, editors,
pages 119-125, A K Peters, 2005.
-
Mark Wainwright,
Prize specimens,
Plus magazine,
01 January 2001,
https://plus.maths.org/content/prize-specimens
Source code:
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tile001_adjacency.m,
adjacency information for tile001.
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tile002_adjacency.m,
adjacency information for tile002.
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tile003_adjacency.m,
adjacency information for tile003.
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tile004_adjacency.m,
adjacency information for tile004.
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tile005_adjacency.m,
adjacency information for tile005.
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tile006_adjacency.m,
adjacency information for tile006.
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tile007_adjacency.m,
adjacency information for tile007.
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tile008_adjacency.m,
adjacency information for tile008.
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tile009_adjacency.m,
adjacency information for tile009.
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tile010_adjacency.m,
adjacency information for tile010.
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tile011_adjacency.m,
adjacency information for tile011.
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tile012_adjacency.m,
adjacency information for tile012.
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tile013_adjacency.m,
adjacency information for tile013.
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tile014_adjacency.m,
adjacency information for tile014.
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tile015_adjacency.m,
adjacency information for tile015.
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tile016_adjacency.m,
adjacency information for tile016.
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tile017_adjacency.m,
adjacency information for tile017.
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tile018_adjacency.m,
adjacency information for tile018.
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tile019_adjacency.m,
adjacency information for tile019.
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tile020_adjacency.m,
adjacency information for tile020.
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tile021_adjacency.m,
adjacency information for tile021.
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tile022_adjacency.m,
adjacency information for tile022.
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tile023_adjacency.m,
adjacency information for tile023.
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tile024_adjacency.m,
adjacency information for tile024.
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tile025_adjacency.m,
adjacency information for tile025.
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tile026_adjacency.m,
adjacency information for tile026.
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tile027_adjacency.m,
adjacency information for tile027.
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tile028_adjacency.m,
adjacency information for tile028.
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tile029_adjacency.m,
adjacency information for tile029.
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tile030_adjacency.m
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tile031_adjacency.m
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tile032_adjacency.m
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tile033_adjacency.m
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tile034_adjacency.m
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tile035_adjacency.m
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tile036_adjacency.m
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tile037_adjacency.m
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tile038_adjacency.m
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tile039_adjacency.m
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tile040_adjacency.m
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tile041_adjacency.m
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tile042_adjacency.m
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tile043_adjacency.m
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tile044_adjacency.m
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tile045_adjacency.m
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tile046_adjacency.m
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tile047_adjacency.m
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tile048_adjacency.m
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tile049_adjacency.m
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tile050_adjacency.m
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tile051_adjacency.m
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tile052_adjacency.m
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tile053_adjacency.m
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tile054_adjacency.m
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tile055_adjacency.m
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tile056_adjacency.m
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tile057_adjacency.m
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tile058_adjacency.m
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tile059_adjacency.m
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tile060_adjacency.m
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tile061_adjacency.m
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tile062_adjacency.m
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tile063_adjacency.m
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tile064_adjacency.m
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tile065_adjacency.m
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tile066_adjacency.m
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tile067_adjacency.m
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tile068_adjacency.m
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tile069_adjacency.m
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tile070_adjacency.m
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tile071_adjacency.m
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tile072_adjacency.m
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tile073_adjacency.m
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tile074_adjacency.m
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tile075_adjacency.m
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tile076_adjacency.m
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tile077_adjacency.m
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tile078_adjacency.m
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tile079_adjacency.m
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tile080_adjacency.m
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tile081_adjacency.m
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tile082_adjacency.m
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tile083_adjacency.m
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tile084_adjacency.m
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tile085_adjacency.m
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tile086_adjacency.m
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tile087_adjacency.m
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tile088_adjacency.m
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tile089_adjacency.m
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tile090_adjacency.m
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tile091_adjacency.m
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tile092_adjacency.m
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tile093_adjacency.m
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tile094_adjacency.m
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tile095_adjacency.m
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tile096_adjacency.m
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tile097_adjacency.m
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tile098_adjacency.m
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tile099_adjacency.m
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tile100_adjacency.m
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tile101_adjacency.m
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tile102_adjacency.m
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tile103_adjacency.m
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tile104_adjacency.m
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tile105_adjacency.m
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tile106_adjacency.m
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tile107_adjacency.m
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tile108_adjacency.m
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tile109_adjacency.m
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tile110_adjacency.m
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tile111_adjacency.m
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tile112_adjacency.m
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tile113_adjacency.m
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tile114_adjacency.m
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tile115_adjacency.m
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tile116_adjacency.m
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tile117_adjacency.m
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tile118_adjacency.m
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tile119_adjacency.m
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tile120_adjacency.m
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tile121_adjacency.m
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tile122_adjacency.m
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tile123_adjacency.m
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tile124_adjacency.m
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tile125_adjacency.m
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tile126_adjacency.m
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tile127_adjacency.m
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tile128_adjacency.m
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tile129_adjacency.m
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tile130_adjacency.m
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tile131_adjacency.m
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tile132_adjacency.m
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tile133_adjacency.m
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tile134_adjacency.m
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tile135_adjacency.m
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tile136_adjacency.m
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tile137_adjacency.m
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tile138_adjacency.m
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tile139_adjacency.m
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tile140_adjacency.m
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tile141_adjacency.m
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tile142_adjacency.m
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tile143_adjacency.m
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tile144_adjacency.m
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tile145_adjacency.m
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tile146_adjacency.m
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tile147_adjacency.m
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tile148_adjacency.m
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tile149_adjacency.m
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tile150_adjacency.m
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tile151_adjacency.m
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tile152_adjacency.m
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tile153_adjacency.m
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tile154_adjacency.m
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tile155_adjacency.m
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tile156_adjacency.m
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tile157_adjacency.m
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tile158_adjacency.m
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tile159_adjacency.m
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tile160_adjacency.m
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tile161_adjacency.m
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tile162_adjacency.m
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tile163_adjacency.m
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tile164_adjacency.m
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tile165_adjacency.m
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tile166_adjacency.m
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tile167_adjacency.m
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tile168_adjacency.m
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tile169_adjacency.m
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tile170_adjacency.m
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tile171_adjacency.m
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tile172_adjacency.m
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tile173_adjacency.m
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tile174_adjacency.m
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tile175_adjacency.m
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tile176_adjacency.m
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tile177_adjacency.m
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tile178_adjacency.m
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tile179_adjacency.m
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tile180_adjacency.m
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tile181_adjacency.m
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tile182_adjacency.m
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tile183_adjacency.m
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tile184_adjacency.m
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tile185_adjacency.m
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tile186_adjacency.m
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tile187_adjacency.m
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tile188_adjacency.m
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tile189_adjacency.m
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tile190_adjacency.m
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tile191_adjacency.m
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tile192_adjacency.m
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tile193_adjacency.m
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tile194_adjacency.m
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tile195_adjacency.m
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tile196_adjacency.m
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tile197_adjacency.m
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tile198_adjacency.m
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tile199_adjacency.m
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tile200_adjacency.m
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tile201_adjacency.m
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tile202_adjacency.m
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tile203_adjacency.m
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tile204_adjacency.m
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tile205_adjacency.m
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tile206_adjacency.m
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tile207_adjacency.m
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tile208_adjacency.m
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tile209_adjacency.m
Last revised on 18 April 2024.