Low-Complexity Tilings of the Plane
Discrete Mathematics
2019-05-13 v1 Combinatorics
Dynamical Systems
Abstract
A two-dimensional configuration is a coloring of the infinite grid Z^2 with finitely many colors. For a finite subset D of Z^2, the D-patterns of a configuration are the colored patterns of shape D that appear in the configuration. The number of distinct D-patterns of a configuration is a natural measure of its complexity. A configuration is considered having low complexity with respect to shape D if the number of distinct D-patterns is at most |D|, the size of the shape. This extended abstract is a short review of an algebraic method to study periodicity of such low complexity configurations.
Cite
@article{arxiv.1905.04183,
title = {Low-Complexity Tilings of the Plane},
author = {Jarkko Kari},
journal= {arXiv preprint arXiv:1905.04183},
year = {2019}
}
Comments
21st International Conference on Descriptional Complexity of Formal Systems (DCFS 2019) invited paper