A strongly aperiodic set of tiles in the hyperbolic plane

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. © Springer-Verlag 2004.