Wang, Xingyuan; Liu, Xiangdong; Zhu, Weiyong Researches on general Mandelbrot sets from complex map \(z\leftarrow z^a+c (\alpha<0)\). (Chinese. English summary) Zbl 0922.28008 Acta Math. Sci. (Chin. Ed.) 19, No. 1, 73-79 (1999). 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. Cited in 4 Documents MSC: 28A80 Fractals 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:escape time algorithm; Mandelbrot sets; complex mapping PDFBibTeX XMLCite \textit{X. Wang} et al., Acta Math. Sci. (Chin. Ed.) 19, No. 1, 73--79 (1999; Zbl 0922.28008)