Homogeneity of subjective cellular automata

Abstract

We bring out some similarities among one-dimensional surjective cellular automata. Four main results are the following: (i) all periodic points of a cellular automata are shift-periodic if and only if the set of periodic points of any fixed period is finite, (ii) forward recurrent points as well as backward recurrent points are residual for every onto cellular automata, (iii) every onto cellular automata is semi-open, and (iv) all transitive cellular automata are weak mixing and hence maximally sensitive (which improves an existing result).