Patch frequencies in Penrose rhombic tilings
Dynamical Systems
2025-10-22 v2 Mathematical Physics
math.MP
Abstract
This short exposition presents an algorithm for an exact calculation of patch frequencies for the rhombic Penrose tiling. We recall a construction of Penrose tilings via dualisation, and by extending the known method for obtaining vertex configurations, we obtain the desired algorithm. It is then used to determine the frequencies of several particular large patches which appear in the literature. The analogous approach is also explained for the Ammann-Beenker tiling.
Keywords
Cite
@article{arxiv.2212.09406,
title = {Patch frequencies in Penrose rhombic tilings},
author = {Jan Mazáč},
journal= {arXiv preprint arXiv:2212.09406},
year = {2025}
}
Comments
30 pages, 26 figures, 2 tables (minor changes)