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Researches on general Mandelbrot sets from complex map \(z\leftarrow z^a+c (\alpha<0)\). (Chinese. English summary) Zbl 0922.28008

Summary: This paper expounds the escape time algorithm of constructing general Mandelbrot sets from the complex mapping \(z \leftarrow z^\alpha+ c (\alpha<0)\). A series of interesting and rich families of fractal images are generated by changing a single parameter \(\alpha\). 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 satellitic structure arising for non-integer values of \(\alpha\) are also analysed. At the end, some conclusions are made.

MSC:

28A80 Fractals
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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