Aperiodic Tiling

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The informal term aperiodic tiling loosely refers to both an aperiodic set of tiles, and to the tilings which such sets admit. Properly speaking, aperiodicity is a property of the set of tiles themselves; any given finite tiling is either periodic or non-periodic. Further confusing the matter is that a given aperiodic set of tiles typically admits infinitely many distinct tilings. One proposed formal definition is that a tiling of the plane is aperiodic if and only if it consists of copies of a finite set of tiles, that themselves only admit non-periodic tilings.

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High Quality Content by WIKIPEDIA articles! The informal term aperiodic tiling loosely refers to both an aperiodic set of tiles, and to the tilings which such sets admit. Properly speaking, aperiodicity is a property of the set of tiles themselves; any given finite tiling is either periodic or non-periodic. Further confusing the matter is that a given aperiodic set of tiles typically admits infinitely many distinct tilings. One proposed formal definition is that a tiling of the plane is aperiodic if and only if it consists of copies of a finite set of tiles, that themselves only admit non-periodic tilings.