Diffraction of the Hat and Spectre tilings and some of their relatives
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911188223262720 |
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| author | Baake, Michael Gähler, Franz Mazáč, Jan Mitchell, Andrew |
| author_facet | Baake, Michael Gähler, Franz Mazáč, Jan Mitchell, Andrew |
| contents | The diffraction spectra of the Hat and Spectre monotile tilings, which are known to be pure point, are derived and computed explicitly. This is done via model set representatives of self-similar members in the topological conjugacy classes of the Hat and the Spectre tiling, which are the CAP and the CASPr tiling, respectively. This is followed by suitable reprojections of the model sets to represent the original Hat and Spectre tilings, which also allows to calculate their Fourier--Bohr coefficients explicitly. Since the windows of the underlying model sets have fractal boundaries, these coefficients need to be computed via an exact renormalisation cocycle in internal space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffraction of the Hat and Spectre tilings and some of their relatives Baake, Michael Gähler, Franz Mazáč, Jan Mitchell, Andrew Metric Geometry Mathematical Physics 52C23, 42A38 The diffraction spectra of the Hat and Spectre monotile tilings, which are known to be pure point, are derived and computed explicitly. This is done via model set representatives of self-similar members in the topological conjugacy classes of the Hat and the Spectre tiling, which are the CAP and the CASPr tiling, respectively. This is followed by suitable reprojections of the model sets to represent the original Hat and Spectre tilings, which also allows to calculate their Fourier--Bohr coefficients explicitly. Since the windows of the underlying model sets have fractal boundaries, these coefficients need to be computed via an exact renormalisation cocycle in internal space. |
| title | Diffraction of the Hat and Spectre tilings and some of their relatives |
| topic | Metric Geometry Mathematical Physics 52C23, 42A38 |
| url | https://arxiv.org/abs/2502.03268 |