Danzer-like tilings with infinite local complexity

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Other

Publication Date

6-2024

Abstract

In this presentation, a construction of a class of substitution tilings will be shown. The inflation factor is the longest diagonal of a regular � −gon, � ∈ {13, 17, 21}, and belongs to the family of inflation factors described by Nishcke and Danzer in [4]. To obtain a dissection of the substitution, we apply the Kannan-Soroker-Kenyon criterion [2, 3], along with some tile orientation conditions to guarantee that the tiling has � −fold dihedral symmetry. We then use Danzer’s algorithm [1] to prove that the tiling has infinite local complexity. The algorithm assumes that the inflation factor is not Pisot. The main idea is to look for a misfit situation in a supertile of the substitution and iterate the substitution on a patch that contains the misfit situation, giving rise to infinitely many two-tile patches corresponding to the substitution.

html

Disciplines

Mathematics | Statistics and Probability

Note

Abstract and presentation slides only

Keywords

Tiling (Mathematics)

Upload File

wf_no

This document is currently not available here.

Share

COinS