Tilings Robust to Errors

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 (see [6,7]). 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.

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Alexis Ballier, Bruno Durand, Emmanuel Jeandel
• Keywords: Error Robustness, Fundamental Question, Information Retrieval, LATIN 2010, Periodic Tilings