A note on cellular automata

Abstract

In this note, we give a new totally topological definition of cellular automata over groups. We show that every continuous self-map of the shift space A^G can be represented as a G-sequence of cellular automata. In the case of a finitely generated group G and a finite alphabet A, we prove that the set of all cellular automata is discrete in the uniform metric space of continuous self-maps of A^G.

Keywords

• cellular automata
• symbolic dynamic
• dynamical system