逃逸区间分类法构造广义M-J混沌分形图谱的研究

Structure of M-J chaos fractal graphic spectrum based on escape region classification algorithm

在对传统的复映射z←zα+c(α∈R)广义M-集计算机算法的研究基础上,分析了几种常用的算法,提出了一种改进的逃逸区间分类法来绘制广义M-集,并给出上述算法生成的图像。通过大量的计算机数学实验,表明采用该算法绘制的混沌分形图谱能够更加直观地描绘出广义M-集对应轨道的收敛区间,为进一步揭开广义M-集的内部形成机理提供了一个新的研究方法。

On the basis of constructing computer algorithms of general Mandelbrot set of the complex mapping:zz~α+c(α∈R),several usual algorithm were analyzed.Furthermore,a new improved escape region classification algorithm was raised to draw general Mandelbrot set,and images generated with the algorithms above were shown.Through computer math experiments,it is proved that general Mandelbrot set protracted with the new algorithm describe new stability information of Mandelbrot set orbit more definitely.It is a new method to discover the mechanism of general Mandelbrot set.