Cáceres González, JoséMárquez Pérez, Alberto2016-02-092016-02-092002Cáceres González, J. y Márquez Pérez, A. (2002). An aperiodic tiles machine. Computational Geometry, 23, 171-182.http://hdl.handle.net/11441/34382The 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Penrose tilingsMatching rulesLocal isomorphismVoronoi diagramAperiodic prototilesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/S0925-7721(01)00060-8