An aperiodic tiles machine

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 examp...

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Detalles Bibliográficos
Autores: Cáceres González, José, Márquez Pérez, Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2002
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/34382
Acceso en línea:http://hdl.handle.net/11441/34382
https://doi.org/10.1016/S0925-7721(01)00060-8
Access Level:acceso abierto
Palabra clave:Penrose tilings
Matching rules
Local isomorphism
Voronoi diagram
Aperiodic prototiles
Descripción
Sumario: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.