Abstract
Cellular automata are dynamical systems on the compact metric space of subshifts. They leave many classes of subshifts invariant. Here we show that cellular automata leave 'circle subshifts' invariant. These are the strictly ergodic subshifts of (0,1)(Zd) obtained by a circle sequence xn=1J(n. alpha ) where J is a finite union of half-open intervals. For such initial conditions, the evolution of the whole infinite configuration can be computed by evolving the finitely many parameters defining the set J. Moreover, many macroscopic quantities can be computed exactly for the infinite system. We illustrate that in one dimension by rule 18 and in two dimensions by the Game of Life. The ideas also apply to cellular automata acting on (0, ..., N-1)(Zd). This we illustrate by the HPP model, a lattice gas automaton with N=16.