构造高阶广义M─分形图及对称逃逸时间算法

Constructed General High order Mandelbrot Fractal Images and Symmetrical Escape Time Algorithm

利用“对称逃逸时间算法”，根据经典的“Ｍａｎｄｅｌｂｒｏｔ－集”的构造方法，构造了一系列高阶多项式的复映射变换：ｆ（ｚ）＝ｚｍ＋ｃ（２≤ｍ≤１０）所显示的高阶广义Ｍａｎｄｅｌｂｒｏｔ－集（简称Ｍ－集或Ｍ－分形图），提供对其定量研究的新材料．这些独特而奇妙的分形图不仅特别令人赏心悦目，而且“

According to the principle of constructing typical Mandelbrot set,this paper constructs a series of general high order Mandelbrot sets of the high order polynomial complex maps f(z)=z m+c(2≤m≤10) by 'symmetrical escape time algorithm' and provides new materials to study them quantitatively. These marvelous fractal images are not only attractive,but also called 'one of the most complicated research object in the mathematic field'.