Nonperiodic tilings related to Stern's diatomic series and based on tiles decorated with elements of $\mathbb{F}_p$
Abstract
This paper presents the construction and various properties of substitution tilings related to Stern's diatomic series and based on tiles decorated with elements of $\mathbb{F}_p$ for some odd prime number $p$. These substitution tilings are additive in a sense that will be clarified later and lead to new nonperiodic tilings in one and two dimensions.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.06039
- arXiv:
- arXiv:2301.06039
- Bibcode:
- 2023arXiv230106039S
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Number Theory;
- 05B45
- E-Print:
- 54 pages, 62 figures