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An aperiodic tiles machine

By José Cáceres González and Alberto Márquez Pérez


The results we introduce in this work lead to get an algorithm which produces aperiodic sets of tiles using Voronoi diagrams. This algorithm runs in optimal worst-case time O(nlogn). Since a wide range of new examples can be obtained, it could shed some new light on non-periodic tilings. These examples are locally isomorphic and exhibit the 5-fold symmetry which appears in Penrose tilings and quasicrystals. Moreover, we outline a similar construction using Delaunay triangulations and propose some related open problems

Topics: Penrose tilings, Matching rules, Local isomorphism, Voronoi diagram, Aperiodic prototiles
Year: 2002
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