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

Abstract 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.

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