Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aperiodic tilings with one prototile and low complexity atlas matching
  rules   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.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex