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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- 1.Berger, R.: The undecidability of the Domino Problem. Mem. Am. Math. Soc. 66 (1966)Google Scholar
- 3.Epstein, D., et al.: Word processing in groups. Boston: Jones and Bartlett 1992Google Scholar
- 4.Goodman-Strauss, C.: Open questions in tilings. PreprintGoogle Scholar
- 5.Goodman-Strauss, C.: Regular production systems and triangle tilings. PreprintGoogle Scholar
- 6.Grünbaum, B., Shepherd, G.C.: Tilings and patterns. New York: W.H. Freeman and Co. 1987Google Scholar
- 13.Wang, H.: Proving theorems by pattern recognition II. Bell System Tech. J. 40, 1–42 (1961)Google Scholar