einstein-tiling

Generate aperiodic tilings by the hat monotile as SVG images, using the clusters and matching rules of Smith, Myers, Kaplan and Goodman-Strauss, An aperiodic monotile.

It has no dependencies, and uses exact integer coordinates throughout.

Command line

$ einstein-tiling tiling --level 4 -o tiling.svg
$ einstein-tiling tiling --level 3 --metatiles --no-crop -o patch.svg
$ einstein-tiling clusters -o clusters.svg
$ einstein-tiling check --level 5
$ einstein-tiling tiling --colour 'H=#d0e4f5' --colour reflected=navy -o tiling.svg

The colour names are H, T, P and F for the hats in each kind of cluster, reflected for the reflected hats, outline, metatile and background. Any SVG colour works, including none.

Python

import einstein_tiling as et

tiles = et.supertile("H", level=4)
assert not et.label_violations(tiles)

with open("tiling.svg", "w") as f:
    f.write(et.tiling_svg(tiles, width=1200, colours={"reflected": "navy"}))

for cluster, reflected, vertices in et.hat_polygons(tiles):
    ...  # Each hat's (x, y) vertices, for use with any plotting library.

Citing

If you use this software, please cite it, and the papers it implements: GitHub's "Cite this repository" button gives the details from CITATION.cff.

• David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss, "An aperiodic monotile", Combinatorial Theory 4(1) (2024), doi:10.5070/C64163843.

Licence

BSD-3-Clause. The substitution rules are adapted from hatviz by Craig S. Kaplan: see LICENSES/hatviz-BSD-3-Clause.txt.