Patch frequencies in Penrose rhombic tilings
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912661081423872 |
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| author | Mazáč, Jan |
| author_facet | Mazáč, Jan |
| contents | This short exposition presents an algorithm for an exact calculation of patch frequencies for the rhombic Penrose tiling. We recall a construction of Penrose tilings via dualisation, and by extending the known method for obtaining vertex configurations, we obtain the desired algorithm. It is then used to determine the frequencies of several particular large patches which appear in the literature. The analogous approach is also explained for the Ammann-Beenker tiling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09406 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Patch frequencies in Penrose rhombic tilings Mazáč, Jan Dynamical Systems Mathematical Physics 37B52, 52C23 This short exposition presents an algorithm for an exact calculation of patch frequencies for the rhombic Penrose tiling. We recall a construction of Penrose tilings via dualisation, and by extending the known method for obtaining vertex configurations, we obtain the desired algorithm. It is then used to determine the frequencies of several particular large patches which appear in the literature. The analogous approach is also explained for the Ammann-Beenker tiling. |
| title | Patch frequencies in Penrose rhombic tilings |
| topic | Dynamical Systems Mathematical Physics 37B52, 52C23 |
| url | https://arxiv.org/abs/2212.09406 |