Aperiodic monotile
An aperiodic monotile (sometimes called an "einstein") is a shape that can tile the plane, but every such tiling is necessarily non-periodic.[1][2] In layman's terms, it is a tile that can be used to cover a flat surface without any overlapping or gaps, but does not show any periodic repetition.
A famous example is the "hat" aperiodic monotile, discovered in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss.[2] The "hat" tile forces aperiodicity in the plane; however, all tilings by the hat require both mirror images of the tile to appear. Later in 2023, the same authors published a paper presenting the discovery of a "spectre" aperiodic monotile, which tiles aperiodically using only translations and rotations, even when reflections are permitted.[3][4]
Also see
References
- ↑ "Aperiodic monotile". Complex Projective 4-Space (March 21, 2023).
- ↑ 2.0 2.1 "An aperiodic monotile".
- ↑ "A chiral aperiodic monotile".
- ↑ "Miscellaneous discoveries". Complex Projective 4-Space (July 23, 2023).
External links
- "An aperiodic monotile exists!". The Aperiodical (March 22, 2023).
- Aperiodic tiling at Wikipedia
- Einstein problem at Wikipedia