Cyclotomic Aperiodic Substitution Tilings with Dense Tile Orientations

2019/01/22 by Stefan Pautze, Pautze, Stefan
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · #05B45 #52C20 #52C23 #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1901.07639

openalex publication_date 2019/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The class of Cyclotomic Aperiodic Substitution Tilings (CAST) whose vertices are supported by the 2n-th cyclotomic field ℚ(ζ_2n) 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 (kπ)/(2n)≠arg(η)∉\mathbbπQ. 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∈\ 2,3,4,5,6,7\ . The examples for n∈\ 2,3,4,5,6\ also yield finite local complexity (FLC).

Citations

• The Pinwheel Tilings of the Plane

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