The computation of overlap coincidence in Taylor-Socolar substitution tiling
Metric Geometry
2012-12-19 v1 Mathematical Physics
math.MP
Abstract
Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \cite{AL} to check overlap coincidence. It turns out that the tiling has overlap coincidence. So the tiling dynamics has pure point spectrum and we can conclude that this tiling has a quasicrystalline structure.
Keywords
Cite
@article{arxiv.1212.4209,
title = {The computation of overlap coincidence in Taylor-Socolar substitution tiling},
author = {Shigeki Akiyama and Jeong-Yup Lee},
journal= {arXiv preprint arXiv:1212.4209},
year = {2012}
}
Comments
8pages, 2 figures