Octagonal tilings with three prototiles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929700873437184 |
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| author | Say-awen, April Lynne D. Coates, Sam |
| author_facet | Say-awen, April Lynne D. Coates, Sam |
| contents | Motivated by theoretically and experimentally observed structural phases with octagonal symmetry, we introduce a family of octagonal tilings which are composed of three prototiles. We define our tilings with respect to two non-negative integers, $m$ and $n$, so that the inflation factor of a given tiling is $δ_{(m,n)}=m+n (1+\sqrt{2})$. As such, we show that our family consists of an infinite series of tilings which can be delineated into separate `cases' which are determined by the relationship between $m$ and $n$. Similarly, we present the primitive substitution rules or decomposition of our prototiles, along with the statistical properties of each case, demonstrating their dependence on these integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Octagonal tilings with three prototiles Say-awen, April Lynne D. Coates, Sam Soft Condensed Matter Other Condensed Matter Mathematical Physics Motivated by theoretically and experimentally observed structural phases with octagonal symmetry, we introduce a family of octagonal tilings which are composed of three prototiles. We define our tilings with respect to two non-negative integers, $m$ and $n$, so that the inflation factor of a given tiling is $δ_{(m,n)}=m+n (1+\sqrt{2})$. As such, we show that our family consists of an infinite series of tilings which can be delineated into separate `cases' which are determined by the relationship between $m$ and $n$. Similarly, we present the primitive substitution rules or decomposition of our prototiles, along with the statistical properties of each case, demonstrating their dependence on these integers. |
| title | Octagonal tilings with three prototiles |
| topic | Soft Condensed Matter Other Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2502.04133 |