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Inventiones mathematicae

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

A strongly aperiodic set of tiles in the hyperbolic plane

  • Chaim Goodman-Strauss
Article

Abstract

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.

Keywords

Production System Periodic Orbit Hyperbolic Plane Regular Production Cyclic Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArkansasFayettevilleUSA

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