eternity_tile
eternity_tile,
a MATLAB 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 monotiles.
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,
a MATLAB 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,
a MATLAB 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,
a MATLAB code which
considers polyiamonds, simple connected shapes constructed from
equilateral triangles connected edgewise.
polyominoes,
a MATLAB 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,
a MATLAB 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
-
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.