Classification of directional dynamics for 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 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.