A strongly aperiodic set of tiles in the hyperbolic plane
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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”  that does admit bi-infinite orbits, but admits no periodic orbits.
KeywordsProduction System Periodic Orbit Hyperbolic Plane Regular Production Cyclic Symmetry
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