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.

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.