CAP

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A substitution for the aperiodic hat monotile found in 2022 and published in [SMCG2024] , see also [BGS2023] . The “metatiles” in the first paper have some free parameter. Most of these parameters yield a substitution that is not selfsimilar. Here we show the selfsimilar version of the substitution rule. This tiling was used to derive the cut-and-project description of the hat tiling in [BGS2023] .

Substitution Rule

Rule CAP

Patch

Patch CAP download vectorformat CAP

References

[SMCG2024]
Smith, D. and Myers, J. S. and Kaplan, C. S. and Goodman-Strauss, C.
An Aperiodic Monotile
Combinatorial Theory 2024, 4(1), https://doi.org/10.5070/C64163843

[BGS2023]
Baake, M. and Gähler, F. and Sadun, L.
Dynamics and topology of the Hat family of tilings
(submitted)