Automaticity and invariant measures of linear cellular automata

11/03/2018

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by   Eric Rowland, et al.

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We show that spacetime diagrams of linear cellular automata Φ with (-p)-automatic initial conditions are automatic. This extends existing results on initial conditions which are eventually constant. Each automatic spacetime diagram defines a (σ, Φ)-invariant set in F_p^ Z, where σ is the left shift map, and if the initial condition is not eventually periodic then this invariant set is nontrivial. We also construct, for the Ledrappier cellular automaton, a family of nontrivial (σ, Φ)-invariant measures.