International journal of bifurcation and chaos vol:9 issue:1 pages:67-95
We consider one-dimensional linear cellular automata whose states are the integers module a prime power p(d) and their orbital patterns. We are particulary interested in initial states and their orbital patterns which are invariant under a certain coarse-graining operation. We show that these coarse-graining invariant initial states are p-automatic. The relationship between the solutions of a certain family of coarse-graining invariant problems concerning linear cellular automata over the integers module p(n) is investigated.