复映射Z←Z~α+C(α<0)所构造的广义M-集中B^(k′)的自相似嵌套研究

Self Similar Nestification of B^(k′) in General Mandelbrot Sets Generated by the Complex Map Z←Z~α+C(α<0)

研究了复映射Z←Zα+C(α <0 )所产生的广义Mandelbrot集的内部结构 ,利用逃逸时间算法改变参数α,作出一系列分形图 ,通过具体的实验数据论证了这些分形图中逃逸点的分布规律 ,特别阐述了其中Bk′ 偏卫星系自相似嵌套规律·

The inner structure of the general Mandelbrot sets generated by the complex map Z←Z α+C(α <0) was studied. A series of families of fractal images were generated by using the escape time algorithm and changing a single parameter. The distributing rule of the escaping points was proved by using material data. The rule of self similar nestification of partial satellite galaxy B k′ was brought forward.