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Low-Complexity Tilings of the Plane

Name: Low-Complexity Tilings of the Plane
Creator: Kari, Jarkko
Keywords: Pattern complexity, FOS: Computer and information sciences, Periodicity, Algebraic subshifts, Discrete Mathematics (cs.DM), ta111, 37B50, G.2.1, Dynamical Systems (math.DS), 0102 computer and information sciences

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint , Conference object 01 Jan 2019Embargo end date: 01 Jan 2019Publisher:Springer International Publishing

Authors: Kari, Jarkko;

doi: 10.1007/978-3-030-23247-4_2 , 10.48550/arxiv.1905.04183

arXiv: http://arxiv.org/abs/1905.04183

Low-Complexity Tilings of the Plane

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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.

21st International Conference on Descriptional Complexity of Formal Systems (DCFS 2019) invited paper

Related Organizations

University of Turku
Finland

Keywords

Pattern complexity, FOS: Computer and information sciences, Periodicity, Algebraic subshifts, Discrete Mathematics (cs.DM), ta111, 37B50, G.2.1, Dynamical Systems (math.DS), Low complexity subshifts, [INFO] Computer Science [cs], G.2.1; F.4.3, Low complexity configurations, F.4.3, FOS: Mathematics, Nivat’s conjecture, Mathematics - Combinatorics, Domino problem, Combinatorics (math.CO), Commutative algebra, Mathematics - Dynamical Systems, Computer Science - Discrete Mathematics

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