Aperiodic monotile

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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


  1. "Aperiodic monotile". Complex Projective 4-Space (March 21, 2023).
  2. 2.0 2.1 "An aperiodic monotile".
  3. "A chiral aperiodic monotile".
  4. "Miscellaneous discoveries". Complex Projective 4-Space (July 23, 2023).

External links