Periodicity and Transitivity for Cellular Automata in Besicovitch Topologies

The Dynamics of Cellular Automata in Shift-Invariant Topologies

We study the dynamics of cellular automata, and more specifically their transitivity and expansivity, when the set of configurations is endowed with a shift-invariant (pseudo-)distance. We first give an original proof of the non-transitivity of cellular automata when the set of configurations is endowed with the Besicovitch pseudo-distance. We then show that the Besicovitch pseudo-distance indu...

On the sensitivity of additive cellular automata in Besicovitch topologies

UNIFORM AND SEMI-UNIFORM TOPOLOGY ON GENERAL FUZZY AUTOMATA

In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of ...

Cellular Automata in the Cantor, Besicovitch, and Weyl Topological Spaces

The Besicovitch and Weyl pseudometrics on the space AŸ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from A by factoring through the equivalence of zero distance. Cellular automata are considered as dynamical systems on the Besicovitch and Weyl spaces and their topological a...

Geometry and Dynamics of the Besicovitch and Weyl Spaces

We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition, we study canonical projections into subshifts, characterize the cellular automata that are contracting or isometric in the Besicovitch or Weyl spaces, study continuous functions that locally look like cellular automat...