Abstract
The z-plane fractal images generated from the generalized transformation function z ← z α + c, α < 0, are analyzed. The fractal images consist of planetary structures with a central planet surrounded by satellite structures. The positions and sizes of the planet and satellite structures are analytically estimated. The partial structures arising for non-integer values of α are also analysed. For α greater than a critical value drastic changes occur in the images; these changes are explained.
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