Another proof of the theorem on pattern reproduction in tessellation structures

  • Authors:

  • Peter Gordon Anderson

  • Affiliations:

  • -

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1976

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Abstract

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 E^n 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=X^p+Y^p (mod p) is translated into the notion of pattern reproduction.