A small fraction of cellular automata are like crystals, and the bulk of cellular automata are like ideal gases. The analytical methods used to study crystals are applicable to this first set of automata, and the analytical methods used to study gases are applicable to the second set of automata. In particular, the mean field theory is an excellent approximation for many cellular automata. Between these extremes lie the liquids on one hand, and the interesting cellular automata on the other. Here correlations between entites exist, but tend to decay with distance at a finite, but non-zero rate.
Entities cooperate to form macroscopic patterns, often shifting and unstable.
The assumptions of the mean field theory are no longer valid. Analysis must take the sharing of information between entities into account explicitly. References H.A. Gutowitz Cellular Automata which Possess a Natural Measure , In preparation.