  Let L:=Z^D be a D-dimensional lattice. Let A^L be the Cantor space of
L-indexed configurations in a finite alphabet A, with the natural L-action by
shifts. A `cellular automaton' is a continuous, shift-commuting self-map
F:A^L-->A^L. An `F-invariant subshift' is a closed, F-invariant and
shift-invariant subset X of A^L. Suppose x is an element of A^L that is
X-admissible everywhere except for some small region of L which we call a
`defect'. Such defects are analogous to `domain boundaries' in a crystalline
solid. It has been empirically observed that these 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.
