Collisions and their Catenations: Ultimately Periodic Tilings of the Plane

Abstract : Motivated by the study of cellular automata algorithmics and dynamics, we investigate an extension of ultimately periodic words to two-dimensional infinite words: collisions. A natural composition operation on tilings leads to a catenation operation on collisions. By existence of aperiodic tile sets, ultimately periodic tilings of the plane cannot generate all possible tilings but exhibit some useful properties of their one-dimensional counterparts: ultimately periodic tilings are recursive, very regular, and tiling constraints are easy to preserve by catenation. We show that, for a given catenation scheme of finitely many collisions, the generated set of collisions is semi-linear.
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Contributor : Gaétan Richard <>
Submitted on : Thursday, August 7, 2008 - 8:56:02 PM
Last modification on : Thursday, April 25, 2019 - 11:26:03 AM
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  • HAL Id : hal-00175397, version 3



Nicolas Ollinger, Gaétan Richard. Collisions and their Catenations: Ultimately Periodic Tilings of the Plane. 2008. ⟨hal-00175397v3⟩



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