On Directional Entropy of a Z 2 -action
نویسنده
چکیده
Consider the cellular automata (CA) of Z 2-action Φ on the space of all doubly infinite sequences with values in a finite set Zr, r ≥ 2 determined by cellular automata T F [−k,k] with an additive automaton rule k i=−k a i x n+i (modr). It is investigated the concept of the measure theoretic directional entropy per unit of length in the direction ω 0. It is shown that hµ(T u F [−k,k]) = uhµ(T F [−k,k]), hµ(Φ u) = uhµ(Φ) and h v (Φ u) = uh v (Φ) for v ∈ Z 2 where h is the measure-theoretic entropy.
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