Tilings robust to errors

Alexis Ballier (1) , Bruno Durand (1) , Emmanuel Jeandel (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

We study the error robustness of tilings of the plane. The fundamental question is the following: given a tileset, what happens if we allow a small probability of errors? Are the objects we obtain close to an error-free tiling of the plane? We prove that tilesets that produce only periodic tilings are robust to errors. For this proof, we use a hierarchical construction of islands of errors. We also show that another class of tilesets, those that admit countably many tilings is not robust and that there is no computable way to distinguish between these two classes.

Domaines: Autre [cs.OH]

Alexis Ballier, Bruno Durand, Emmanuel Jeandel. Tilings robust to errors. 2009. ⟨hal-00430265⟩