Another proof of the theorem on pattern reproduction in tessellation structures

摘要

In this paper a cellular automaton is regarded as a time sequence of polynomials with coefficients in the state alphabet; this is in contrast to the usual view as a mapping of lattice points of En to the state alphabet. The transition from one polynomial to the next can be expressed as a polynomial multiplication. When the state alphabet is the integers modulo a prime p, the theorem (X+Y)p≡Xp+Yp (mod p) is translated into the notion of pattern reproduction.