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...
| Autores: | , |
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| 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 |
| 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. |
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