Abstract
If M is a noninvertible translation-invariant local surjective mapping, it is shown that some local one-dimensional deterministic cellular automaton rules F have a transform Φ by M defined by Φ ∘ M = M ∘ F. When it exists Φ is local and its Wolfram's class is the same as F. The evolution of a cellular automaton according to rule Φ 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 the structure and interactions of the transformed particles for rule Φ are also known. If M is a nontrivial invertible translation-invariant local surjective mapping, Φ always exists, but it is, in general, site- and time-dependent.
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