Aperiodic tiling (nonfiction)
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings.
The Penrose tilings are a well-known example of aperiodic tilings.[1][2] In March 2023, four researchers, Chaim Goodman-Strauss, David Smith, Joseph Samuel Myers and Craig S. Kaplan, announced the discovery of an aperiodic monotile.[3]
Aperiodic tilings serve as mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman[4] who subsequently won the Nobel prize in 2011.[5] However, the specific local structure of these materials is still poorly understood.
Several methods for constructing aperiodic tilings are known.
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External links
- Aperiodic tiling @ Wikipedia
- An aperiodic monotile @ Wikipedia