Aperiodic tilings with one prototile and low complexity atlas matching rules

Details Aperiodic tilings with one prototile and low complexity atlas matching rules Aperiodic tilings with one prototile and low complexity atlas matching rules

2010-03-25

arxiv.org/abs/1003.4909v1

Mathematics

Combinatorics

9 pages, 2 figures

Scientific paper

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 $R^3$ aperiodically, and a pair of square tiles that can only tile $R^2$ aperiodically.

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