Decidability and Periodicity of Low Complexity Tilings

Jarkko Kari & Etienne Moutot
In this paper we study low-complexity colorings (or tilings) of the two-dimensional grid ℤ². A coloring is said to be of low complexity with respect to a rectangle if there exists m,n∈ℕ such that there are no more than mn different rectangular m× n patterns in it. Open since it was stated in 1997, Nivat’s conjecture states that such a coloring is necessarily periodic. Suppose we are given at most nm rectangular patterns of size...
This data repository is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation.