Computational Characterization of Surface Entropies for ℤ² Subshifts of Finite Type
Antonin Callard, Pascal Vanier · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2021
Subshifts of finite type (SFTs) are sets of colorings of the plane that avoid a finite family of forbidden patterns. In this article, we are interested in the behavior of the growth of the number of valid patterns in SFTs. While entropy h corresponds to growths that are squared exponential 2^{hn²}, surface entropy (introduced in Pace’s thesis in 2018) corresponds to the eventual linear term in exponential growths. We give here a characterization of the possible surface entropies of SFTs as the Π₃ real numbers of [0,+∞].