Abstract
Motivated by the study of cellular automata algorithmic 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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Ollinger, N., Richard, G. (2008). Collisions and their Catenations: Ultimately Periodic Tilings of the Plane. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds) Fifth Ifip International Conference On Theoretical Computer Science – Tcs 2008. IFIP International Federation for Information Processing, vol 273. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09680-3_16
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DOI: https://doi.org/10.1007/978-0-387-09680-3_16
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