Danzer-like tilings with infinite local complexity
In this presentation, a construction of a class of substitution tilings will be shown. The inflation factor is the longest diagonal of a regular � −gon, � ∈ {13, 17, 21}, and belongs to the family of inflation factors described by Nishcke and Danzer in [4]. To obtain a dissection of the substitution...
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Animo Repository
2024
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/13834 |
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| Institution: | De La Salle University |
| Summary: | In this presentation, a construction of a class of substitution tilings will be shown. The inflation factor is the longest diagonal of a regular � −gon, � ∈ {13, 17, 21}, and belongs to the family of inflation factors described by Nishcke and Danzer in [4]. To obtain a dissection of the substitution, we apply the Kannan-Soroker-Kenyon criterion [2, 3], along with some tile orientation conditions to guarantee that the tiling has � −fold dihedral symmetry. We then use Danzer’s algorithm [1] to prove that the tiling has infinite local complexity. The algorithm assumes that the inflation factor is not Pisot. The main idea is to look for a misfit situation in a supertile of the substitution and iterate the substitution on a patch that contains the misfit situation, giving rise to infinitely many two-tile patches corresponding to the substitution. |
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