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
obtained by a circle sequence
 ,
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
 .
This we illustrate by the HPP model, a lattice gas automaton with
N=16.
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