TRANSFORMATIONS OF ONE-DIMENSIONAL CELLULAR-AUTOMATON RULES BY TRANSLATION-INVARIANT LOCAL SUBJECTIVE MAPPINGS

If M is a noninvertible translation-invariant local surjective mapping , it is shown that some local one-dimensional deterministic cellular a utomaton rules F have a transform PHI by M defined by PHI . M = M . F. When it exists PHI is local and its Wolfram's class is the same as F. The evolution of a cellular automaton according to rule PHI is simply related to the evolution according to rule F. In the case of class-3 rules, the evolution to the attractor may often be viewed as particle- like structures evolving in a regular background. If the structure of these particles and their interactions for a rule F are known, then th e structure and interactions of the transformed particles for rule PHI are also known. If M is a nontrivial invertible translation-invariant local surjective mapping, PHI always exists, but it is, in general, s ite- and time-dependent.