Patch frequencies in rhombic Penrose tilings

This exposition presents an efficient algorithm for an exact calculation of patch frequencies for rhombic Penrose tilings. A construction of Penrose tilings via dualization is recalled and, by extending the known method for obtaining vertex configurations, the desired algorithm is obtained. It is th...

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Detalles Bibliográficos
Autor principal: Mazáč, Jan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: International Union of Crystallography 2023
Materias:
Research Papers
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10483588/
https://www.ncbi.nlm.nih.gov/pubmed/37485825
http://dx.doi.org/10.1107/S2053273323004990
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author Mazáč, Jan
author_facet Mazáč, Jan
author_sort Mazáč, Jan
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description This exposition presents an efficient algorithm for an exact calculation of patch frequencies for rhombic Penrose tilings. A construction of Penrose tilings via dualization is recalled and, by extending the known method for obtaining vertex configurations, the desired algorithm is obtained. It is then used to determine the frequencies of several particularly large patches which appear in the literature. An analogous approach works for a particular class of tilings and this is also explained in detail for the Ammann–Beenker tiling.
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spelling pubmed-104835882023-09-08 Patch frequencies in rhombic Penrose tilings Mazáč, Jan Acta Crystallogr A Found Adv Research Papers This exposition presents an efficient algorithm for an exact calculation of patch frequencies for rhombic Penrose tilings. A construction of Penrose tilings via dualization is recalled and, by extending the known method for obtaining vertex configurations, the desired algorithm is obtained. It is then used to determine the frequencies of several particularly large patches which appear in the literature. An analogous approach works for a particular class of tilings and this is also explained in detail for the Ammann–Beenker tiling. International Union of Crystallography 2023-07-24 /pmc/articles/PMC10483588/ /pubmed/37485825 http://dx.doi.org/10.1107/S2053273323004990 Text en © Jan Mazáč 2023 https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.
spellingShingle Research Papers
Mazáč, Jan
Patch frequencies in rhombic Penrose tilings
title Patch frequencies in rhombic Penrose tilings
title_full Patch frequencies in rhombic Penrose tilings
title_fullStr Patch frequencies in rhombic Penrose tilings
title_full_unstemmed Patch frequencies in rhombic Penrose tilings
title_short Patch frequencies in rhombic Penrose tilings
title_sort patch frequencies in rhombic penrose tilings
topic Research Papers
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10483588/
https://www.ncbi.nlm.nih.gov/pubmed/37485825
http://dx.doi.org/10.1107/S2053273323004990
work_keys_str_mv AT mazacjan patchfrequenciesinrhombicpenrosetilings

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