Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type
arXiv:1603.05464
Abstract
Using a deterministic version of the self-similar (or hierarchical, or fixed-point ) method for constructing 2-dimensional subshifts of finite type (SFTs), we construct aperiodic 2D SFTs with a unique direction of non-expansiveness and prove that the emptiness problem of SFTs is undecidable even in this restricted case. As an additional application of our method, we characterize the sets of directions that can be the set of non-expansive directions of 2D SFTs.
72 pages, main body of the author's PhD Thesis, most of the results obtained in collaboration with Pierre Guillon