ON EXPLICIT EXPRESSIONS IN ADDITIVE CELLULAR-AUTOMATA THEORY

In the present paper, the problem of additive cellular automata is pos ed as a second-order linear difference equation in two indices-time st ep t and position i subject to a periodicity condition for all t and a n initial condition for t = 0. An explicit solution of this mathematic al problem is obtained by using the method of generating function. Thi s explicit formula enables us to compute the configuration at any time without any explicit simulation. The explicit formula has been derive d for all important additive rules; with the help of these, many salie nt characteristics of the transition may be obtained with surprising e ase. The explicit formula method appears to be very efficient and has possibilities to be applied to diverse situations in cellular automata theory.