We show that for an additive one-dimensional cellular automata on space of all doubly infinitive sequences with values in a finite set S = {0, 1, 2, ..., r-1}, determined by an additive automaton rule f(x ∞ f n-k , ..., x n+k) = (mod r), and a-invariant uniform Bernoulli measure µ, the measure-theoretic entropy of the additive one-dimensional cellular automata with respect to µ is equal to h ∑ − = + k i k n x ∞ f k f ∞ f ∞ f µ () = 2klog r, where k ≥ 1, r-1∈S. We also show that the uniform… CONTINUE READING