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Aperiodic tiling

Specific form of plane tiling in mathematics / From Wikipedia, the free encyclopedia

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[1][2] are the best-known examples of aperiodic tilings.

The Penrose tiling is an example of an aperiodic tiling; every tiling it can produce lacks translational symmetry.

Aperiodic tilings serve as mathematical models for quasicrystals, physical solids that were discovered in 1982 by Dan Shechtman[3] who subsequently won the Nobel prize in 2011.[4] However, the specific local structure of these materials is still poorly understood.

Several methods for constructing aperiodic tilings are known.