JournalsggdVol. 13, No. 2pp. 549–578

On pointwise periodicity in tilings, cellular automata, and subshifts

  • Tom Meyerovitch

    Ben Gurion University of the Negev, Beer-Sheva, Israel
  • Ville Salo

    University of Turku, Finland
On pointwise periodicity in tilings, cellular automata, and subshifts cover

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Abstract

We study implications of expansiveness and pointwise periodicity for certain groups and semigroups of transformations. Among other things we prove that every pointwise periodic finitely generated group of cellular automata is necessarily finite. We also prove that a subshift over any finitely generated group that consists of finite orbits is finite, and related results for tilings of Euclidean space.

Cite this article

Tom Meyerovitch, Ville Salo, On pointwise periodicity in tilings, cellular automata, and subshifts. Groups Geom. Dyn. 13 (2019), no. 2, pp. 549–578

DOI 10.4171/GGD/497