A particularly interesting automaton is Q2R which is defined on a square lattice and yields an energy conserving dynamics for the Ising model. With Uriel Costa we studied the energy transport properties of Q2R by placing the automaton in a gradient as published in J. Stat. Phys., Vol.47, p.597-602 (1987).
It is often of interest to mix randomly two or more cellular automata. With Luciano da Silva we considered such a mixture of two rules having different behaviour and studied the mixing ratio at which appears a phase transition as described in a paper published in Complex Systems, Vol.2, 29-37 (1988).