Analysis of the Complex z-Plane Fractal Images from z - z-a + c for a > 0
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Date
1990
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Abstract
The z-plane fractal images generated from the generalized transformation function z - z[superscript -a] + c, a > 0, are analyzed. The fractal images appear to be planetary structures with a central planet surrounded by satellite structures. The positions and the sizes of the planet and satellite structures are analytically estimated. The partial structures arising for non-integer values of a are analyzed. For a greater than a critical value drastic changes occur in the images and these changes are explained.
Keywords: Fractals, Dynamical Systems, Complex Analysis.