Tilings with Infinite Local Complexity and n-Fold Rotational Symmetry, n=13,17,21
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912541639180288 |
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| author | Say-awen, April Lynne D. |
| author_facet | Say-awen, April Lynne D. |
| contents | A tiling is said to have infinite local complexity (ILC) if it contains infinitely many two-tile patches up to rigid motions. In this work, we provide examples of substitution rules that generate tilings with ILC. The proof relies on Danzer's algorithm, which assumes that the substitution factor is non-Pisot. In addition to ILC, the tiling space of each substitution rule contains a tiling that exhibits (global) n-fold rotational symmetry, n=13,17,21. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tilings with Infinite Local Complexity and n-Fold Rotational Symmetry, n=13,17,21 Say-awen, April Lynne D. Metric Geometry A tiling is said to have infinite local complexity (ILC) if it contains infinitely many two-tile patches up to rigid motions. In this work, we provide examples of substitution rules that generate tilings with ILC. The proof relies on Danzer's algorithm, which assumes that the substitution factor is non-Pisot. In addition to ILC, the tiling space of each substitution rule contains a tiling that exhibits (global) n-fold rotational symmetry, n=13,17,21. |
| title | Tilings with Infinite Local Complexity and n-Fold Rotational Symmetry, n=13,17,21 |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2408.17082 |