Thus when an automaton's width is at its absolute maximum, it is at its true complexity. But to just compare the max intervals in automata is inherently meaningless, since many automata go to infinity. Thus the only way to really compare complexity is to compare the cardinality of the max. I think it's about time that automata have a mathematical basis, and this link is a vital one, for from here we can move to other domains. An important use of this is in comparing processes and rules.
Evolution is a natural process, so it can be modeled as an automaton.
We can prove certain facts about it by using the above method. I just know there is some link. I was considering running a phase-space simulation of cellular automata, and seeing what sort of atttractor it has. Fortunately, it isn't so broad that it includes thermostats. No, a thermostat is not a representative system, nor self-maintaining.