Abstract

Methods of computing Mandelbrot and Julia sets for a variety of nonlinear mappings are described. The original Mandelbrot set is constructed using a quadratic mapping. In this paper this is used as the first step in a numerical investigation of the properties of the Mandelbrot sets and the corresponding Julia sets for higher order mappings. The numerical results suggest several interesting relationships between the order of the mapping chosen and the rotational symmetries of the associated Mandelbrot and Julia sets.

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