Fibonacci序列构造z^(-2)+c广义M-J混沌分形图谱及其标度不变性的研究  

The M-J Chaotic Fractal Images of z^(-2)+c Generated by the Fibonacci Sequence and the Scaling Invariance

作　　者：朱伟勇[1] 宋春林[1] 邓学工[1] 刘向东[2] 于海[1] 李志勇[1] 

机构地区：[1]东北大学计算中心,沈阳110004 [2]大连民族学院计算机系,大连116600

出　　处：《计算机学报》2004年第1期52-57,共6页Chinese Journal of Computers

基　　金：国家自然科学基金 (699740 0 8);国家教育部博士点专项科研基金(2 0 0 0 0 14 5 12 )资助

摘　　要：利用周期分类法绘制了z-2 +c的广义M J集分形图 ,分析了广义M集周期芽苞同分岔图的对应关系 ,发现其广义M集周期芽苞的Fibonacci序列的拓扑不变性 .通过大量计算机数学试验 ,发现了主轴上倍周期芽苞在超吸引点处的符号序列的排列规律 ,给出了构造广义M集任意倍周期芽苞字提升方程的一个算法 ,得到主轴上各倍周期芽苞的超吸引点 ,通过大量计算结果猜测M集倍周期芽苞存在一个普适常数 δ ,Julia集存在一个标度因子 α .The M J chaotic fractal images of z -2 +c is protracted with periodic classification algorithm, and the corresponding relationship between Mandelbrot set’s period buds and bifurcation image is analyzed. It is found that the Fibonacci sequence of Mandelbrot set is uniform topology. The symbol sequences arrangement rule of multiplier periodic buds, which are on principal axis’s super attracted points, is proposed with lots of experiments. A novel algorithm used to construct word lifting formula of M sets’ arbitrary multiplier periodic buds is proposed. The multiplier periodic super attracted points are obtained which are on the principal axis. Further more, it is also found that there exists a general constant of M set and a mark factor of Julia set according to a lot of computing results.

关 键 词：图像分析 图像特征 FIBONACCI序列 广义M-J集 混沌 分形图谱 标度不变性 计算机 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]