Cyclotomic Aperiodic Substitution Tilings
Abstract
The class of Cyclotomic Aperiodic Substitution Tilings (CAST) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry Dn or D2n, i.e. the tiling contains an infinite number of patches of any size with dihedral symmetry Dn or D2n only by iteration of substitution rules on a single tile.
Keywords
Cite
@article{arxiv.1606.06858,
title = {Cyclotomic Aperiodic Substitution Tilings},
author = {Stefan Pautze},
journal= {arXiv preprint arXiv:1606.06858},
year = {2017}
}
Comments
60 pages, 31 figures. Parts of Theorem 2.1 (primitive substitution matrices) and Theorem 2.2 (proof of aperiodicity) were revised. A reference to [Hib15] was added, due to a prior claim regarding the generalized Lancon-Billard tiling