TRANSFORMATIONS OF THE ONE-DIMENSIONAL CELLULAR-AUTOMATA RULE SPACE

We introduce the notion of double permutation in order to study partic ular classes of transformations of the one-dimensional cellular automa ta rule space. These classes of transformations are characterized acco rding to different sets of metrical, language theoretic, and dynamical properties they preserve. Each set of transformations we propose indu ces an equivalence relation over the cellular automata rule space. We give exact results on the cardinality of the quotient sets generated b y these equivalence relations. Finally, we discuss some interesting op en problems. (C) 1997 Elsevier Science B.V.