Aperiodic tilings with one prototile and low complexity atlas matching rules
Combinatorics
2010-03-26 v1
Abstract
We give a constructive method that can decrease the number of prototiles needed to tile a space. We achieve this by exchanging edge to edge matching rules for a small atlas of permitted patches. This method is illustrated with Wang tiles, and we apply our method to present via these rules a single prototile that can only tile aperiodically, and a pair of square tiles that can only tile aperiodically.
Keywords
Cite
@article{arxiv.1003.4909,
title = {Aperiodic tilings with one prototile and low complexity atlas matching rules},
author = {David Fletcher},
journal= {arXiv preprint arXiv:1003.4909},
year = {2010}
}
Comments
9 pages, 2 figures