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-Carlitz sequences of polynomials are considered. These properties are coded in an associated fractal set  the rescaled evolution set. We extend previous results on linear cellular automata with states in a finite field. Applications are given for the sequence of Legendre polynomials and sequences associated with the zero Bessel function.
self-similarity legendre polynomials zero bessel function lucas property m-automaticity