Inventiones mathematicae

, Volume 159, Issue 1, pp 119–132 | Cite as

A strongly aperiodic set of tiles in the hyperbolic plane



We construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a “regular production system” [5] that does admit bi-infinite orbits, but admits no periodic orbits.


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© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArkansasFayettevilleUSA

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