A two-dimensional configuration is a coloring of the infinite grid Z2 with finitely many colors. For a finite subset D of Z2, 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.
CITATION STYLE
Kari, J. (2019). Low-Complexity Tilings of the Plane. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11612 LNCS, pp. 35–45). Springer Verlag. https://doi.org/10.1007/978-3-030-23247-4_2
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