Opened Access An aperiodic tiles machine

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Author: Cáceres González, José
Márquez Pérez, Alberto
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2002
Published in: Computational Geometry, 23 (2), 171-182.
Document type: Article
Abstract: 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.
Cite: Cáceres González, J. y Márquez Pérez, A. (2002). An aperiodic tiles machine. Computational Geometry, 23, 171-182.
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