On the directional dynamics of additive cellular automata

We continue the study of cellular automata (CA) directional dynamics, i.e. , the behavior of the joint action of CA and shift maps. This notion has been investigated for general CA in the case of expansive dynamics by Boyle and Lind; and by Sablik for sensitivity and equicontinuity. In this paper we give a detailed classification for the class of additive CA providing non-trivial examples for some classes of Sablik’s classification. Moreover, we extend the directional dynamics studies by considering also factor languages and attractors.