Discovered Tilings
Spectre
The Spectre tiling was derived from the Hat tiling. While the aperiodic monotiles of the Hat tiling appear in two chiralities, the aperiodic monotiles of the Spectre tiling have the same chirality. As the Hat tiling this one is also not really a substitution tiling.
The patch was generated with the …
Aperiodic Monotile
Hat
A pretty simple aperiodic monotile found in 2022 and published in [SMCG2024] . The tile is a tridecagon (13-gon) built from 16 basic triangles with edge lengths $1,2, \sqrt{3}$. The shape alone ensures that every tiling of the plane you can build from this tile will be aperiodic. In this sense it …
Aperiodic Monotile