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.

In March 2023, four researchers, Chaim Goodman-Strauss, David Smith, Joseph Samuel Myers, and Craig S. Kaplan, announced the discovery of an aperiodic monotile.

Aperiodic tilings serve as mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman who subsequently won the Nobel prize in 2011. However, the specific local structure of these materials is still poorly understood.

Several methods for constructing aperiodic tilings are known.

Fiction cross-reference

• Crimes against mathematical constants
• Gnomon algorithm
• Gnomon Chronicles

Nonfiction cross-reference

• Aperiodic set of prototiles (nonfiction)
• Gnomon Chronicles (nonfiction)
• Prototiles (nonfiction)
• Quasicrystal (nonfiction)
• Tessellation (nonfiction)

External links

• Aperiodic tiling @ Wikipedia
• An aperiodic monotile @ arxiv.org