在阐述由复映射z←zα+c(α<0)所构造的广义Julia集(简称广义J集)定义的基础上,通过改变参数α,作出了一系列负实数阶的广义J分形图,当α为负整数时,广义J分形图呈现为一个由|α|个卫星群环绕中央行星的星群结构;而当α为负小数时,广义J分形图中则出现尺寸与α的小数部分成比例的部分卫星群.同时利用复变函数理论和计算机制图相结合的实验数学方法,研究了广义J集的分形结构特征及其演化过程,进而发现相角θ范围的不同选取导致了广义J集的不同演化,并首次给出了广义J集的4种演化过程.

This paper expounds the definition of the general Julia sets (they are called the general J sets for short) from the complex mappingz←zα+c(α<0). A series of interesting and rich families of fractal images are generated by changing a single parameterα. Whenαis a negative integer the fractal image has a planetary configuration consisting of a central planet with α major satellite structures. For noninteger values ofα, additional embryonic satellite structures, proportional in size to the fractional part ofα, are observed. Using the experimental mathematics method combining the theory of analytic function of one complex variable with computer aided drawing, we have analyzed the structural characteristics and the evolutions of the general J set for negative real index number. That the different evolution of the general J set results from the different choice of principal range for the phase angleθis found, and the four evolutions of the general J set are given for the first time.