Aperiodic Tiling

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only non-periodic tilings. The most widely known examples of aperiodic tilings are those formed by Penrose tiles.

Aperiodic pinwheel tiling, photo by P. Bourke, reproduced with permissionAperiodic pinwheel tiling, photo by P. Bourke, reproduced with permission

The Federation Square buildings in Melbourne, Australia feature an aperiodic pinwheel tiling attributed to Charles Radin. The tiling is illustrated above in a pair of photographs by P. Bourke.

The longstanding open problem of finding an aperiodic monotile was solved by Smith et al. (2023) with the discovery of the hat polykite.

See also

Aperiodic Monotile, Hat Polykite, Penrose Tiles, Wang's Conjecture

Explore with Wolfram|Alpha


Dutch, S. "Aperiodic Tilings." May 29, 2003., E. Jr. "Math Games: Melbourne, City of Math." Sep. 5, 2006., D.; Myers, J. S.; Kaplan, C. S.; and Goodman-Strauss, C. "An Aperiodic Monotile." 20 Mar 2023.

Referenced on Wolfram|Alpha

Aperiodic Tiling

Cite this as:

Weisstein, Eric W. "Aperiodic Tiling." From MathWorld--A Wolfram Web Resource.

Subject classifications