On Elementary Second Order Cellular Automata

The paper performs a first exploration of elementary higher order cellular automata. As a first result we give the index of the equivalence relation induced by the usual set of transformations on the local rule (adapted to the new context) when the order is 2. This reveals that the class of second order CA is to large for the purposes of our paper. Hence, we propose to add a further constraint on the structure of the local rule. We call this new class RESOCA . Finally, we provide several results about the dynamics of a large set of RESOCA .