An aperiodic tiles machine

AbstractThe 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