复映射z←z^w+c(w∈C)的广义J集的外部结构

Exterior Structures of the General Julia Sets from Complex Mapping z←z^w+c(w∈C)

推广了美国Alaska大学Philip教授提出的用来探讨Mandelbrot集外部结构的“区域分解”和“角度分解”方法 ,提出了等势线和色彩调配法 ,并利用这四种方法构造了广义Julia集 (简称广义J集 )的一系列外部结构图·研究表明广义J集的外部结构具有分形特征 ,其断裂的原因是主幅角选取的不连续性·

In order to study some exterior structures of the Mandelbort set,professor Philip at University of Alaska invented 'the regional decomposition method'and 'the angle slicing decomposition method'. These two methods were expanded, and the equipotential line method and the color adjustment method were proposed. A series of exterior structures images of the general Julia sets from complex mapping z←z w+c(w∈C) in the complex Z plane were constructed by means of these four methods. The exterior structures of the general Julia sets have the fractal feature. The reason resulting in the discontinuity and collapse of the exterior structures of the generalized Julia sets is the discontinuity of choice of the principal range of the phase angle.