正实数阶广义M集的外部结构

Exterior Structures of the General Mandelbrot Sets for Positive Real Index Number

推广了Philip所提出的“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一系列正实数阶广义M集的外部结构图·研究了广义M集外部结构的分形特征及演化过程 ,结果表明整数阶广义M集的外部区域具有分形特征 ,小数阶广义M集的外部区域出现了错动和断裂 。

The region decomposition method and the angle decomposition method invented by Philip were expended, and the equipotential line method and the color adjustment method were proposed. A series of exterior structures images of the general Mandelbrot sets for positive real index number were constructed by means of these four methods.The fractal characteristics and the evolutions of exterior structures of the general Mandelbrot sets are analyzed. The results show that the exterior regions of the general Mandelbrot sets for integer index number have the fractal feature; while those for decimal index number have discontinuity and collapse, and their evolutions depend on the choice of the principal range of the phase angle.