Abstract:

 This paper expounds the escape time algorithm of constructing general Mandelbrot sets from the complex mapping z←z^α+c(α<0). A series of interesting and rich families of fractal images are generated by changing a single parameter α. 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 embryonic satellite structure arising for non-integer values of α are also analysed. In the end, a few conclusions are reached.

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