Substitutions and Strongly Deterministic Tilesets
Résumé
Substitutions generate hierarchical colorings of the plane. Despite the non-locality of substitution rules, one can extend them by adding compatible local matching rules to obtain locally checkable color- ings as the set of tilings of finite tileset. We show that the resulting tileset can furthermore be chosen strongly deterministic, a tile being uniquely determined by any two adjacent edges. A tiling by a strongly determin- istic tileset can be locally reconstructed starting from any infinite path that cross every line and column of the tiling.
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