Weak colored local rules for planar tilings
Thomas Fernique, Mathieu Sablik · Ergodic Theory and Dynamical Systems · 2018
A linear subspace $E$ of $\mathbb{R}^{n}$ hascolored local rulesif there exists a finite set of decorated tiles whose tilings are digitizations of $E$ . The local rules areweakif the digitizations can slightly wander around $E$ . We prove that a linear subspace has weak colored local rules if and only if it is computable. This goes beyond previous results, all based on algebraic subspaces. We prove an analogous characterization for sets of linear subspaces, including the set of all the linear subspaces of $\mathbb{R}^{n}$ .