Journal of Statistical Physics, Vol. 56, Nos. 1/2, 1989. p. 99-112.
A formal treatment of some of the properties of deterministic, rule 150, elementary one-dimensional cellular automata (CA) with null boundary conditions is presented. The general form of the characteristic polynomial of the CA global rule transition matrix is obtained. Mathematical relationships between the CA register lengths and the order of the corresponding group or semigroup structures are derived.