On the fractal structure of the rescaled evolution set of Carlitz sequences of polynomials

Self-similarity properties of the coefficient patterns of the so-called m-C arlitz sequences of polynomials are considered. These properties are coded in an associated fractal set - the rescaled evolution set. We extend previo us results on linear cellular automata with states in a finite field. Appli cations are given for the sequence of Legendre polynomials and sequences as sociated with the zero Bessel function. (C) 2000 Elsevier Science B.V. All rights reserved.