Intractable problems in reversible cellular automata

The billiard ball model, a classical mechanical system in which all parameters are real variables, can perform all digital computations. An eight-state, 11-neighbor reversible cellular automaton (an entirely discrete system in which all parameters are integer variables) can simulate this model. One of the natural problems for this system is to determine the shape of a container so that they initial specific distribution of gas molecules eventually leads to a predetermined distribution. This problem if PSPACE-complete. Related intractable and decidable problems are discussed as well