# 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