[Algebraic computation of] additive cellular automata

As discussed on page 951 a step in the evolution of an additive cellular automaton can be thought of as multiplication by a polynomial modulo k. After t steps, therefore, the configuration of such a system is given by PolynomialMod[poly^t, k]. This quantity can be computed using power tree methods (see below), though as discussed on page 609, even more efficient methods are also available. (A similar formalism can be set up for any of the cellular automata with generalized additivity discussed on page 952; see also page 886.)