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arXiv · 1901.07639

Cyclotomic Aperiodic Substitution Tilings with Dense Tile Orientations

Stefan Pautze
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Abstract

The class of Cyclotomic Aperiodic Substitution Tilings (CAST) whose vertices are supported by the $2n$-th cyclotomic field $\mathbb{Q}\left(ζ_{2n}\right)$ is extended to cases with Dense Tile Orientations (DTO). It is shown that every CAST with DTO has an inflation multiplier $η$ with irrational argument so that $\frac{kπ}{2n}\neq\arg\left(η\right)\notin\mathbb{πQ}$. The minimal inflation multiplier $η_{min.irr.}$ is discussed for $n\geqq2$. Examples of CASTs with DTO, minimal inflation multiplier $η_{min.irr.}$ and individual dihedral symmetry $D_{2n}$ are introduced for $n\in\left\{ 2,3,4,5,6,7\right\} $. The examples for $n\in\left\{ 2,3,4,5,6\right\} $ also yield finite local complexity (FLC).

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Stefan Pautze. 2019-01-22. Cyclotomic Aperiodic Substitution Tilings with Dense Tile Orientations. https://arxiv.org/abs/1901.07639

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