%0 Journal Article
%T Aperiodic tilings with one prototile and low complexity atlas matching rules
%A David Fletcher
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1003.4909v1