Spectral Domain Boundaries in Cellular Automata

Let A^ZD be the Cantor space of ZD-indexed configurations in a finite alphabet A, and let ? be the ZD-action of shifts on A^ZD . A cellular automaton is a continuous, [sigma]-commuting self-map [Fi] of A^ZD, and a [Fi]-invariant subshift is a closed, ([Fi,sigma])-invariant subset A c A^ZD . Suppose a e A^ZD is A-admissible everywhere except for some small region we call a defect. It has been empirically observed that such defects persist under iteration of F, and often propagate like `particles' which coalesce or annihilate on contact. We use spectral theory to explain the persistence of some defects under F, and partly explain the outcomes of their collisions.