Entropy of Two-Dimensional Permutative Cellular Automata

In the present paper the author discusses entropy of two symbol nearest neighbor per mutative two-dimensional cellular automata. Entropy of dynamical system is perfect invariant for the weak Bernoulli class, which means that if the entropy has the same value for two dynamical systems there exists a conjugacy between them. On the other hand, the value of entropy of two-dimensional cellular automata is infinite or zero in general. This means that the entropy does not work well for two-dimensional cellular automata. To avoid the problem, the author show that ℤ²-action with a two-dimensional cellular automaton map and a shift has finite entropy.