M-J混沌分形图谱的标度不变性  

Scaling Invariance of M-J Chaos-Fractal Images

作　　者：朱志良[1] 曹林[1] 朱伟勇[1] 曾文曲[2] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004 [2]广东工业大学应用数学系,广东广州510090

出　　处：《东北大学学报（自然科学版）》2002年第4期307-310,共4页Journal of Northeastern University(Natural Science)

基　　金：国家教育部高等学校博士点学科专项科研基金资助项目 (2 0 0 0 0 14 5 12 )

摘　　要：研究了复映射z←z2 +c所产生的M J混沌分形图谱的特征参数 ,利用逃逸时间算法绘制M J混沌分形图谱· 以超吸引周期点为基础 ,通过计算机数学实验计算超吸引周期点之间的距离 ,找到Mandelbrot集的普适常数δ ;通过在M 集上的超吸引周期点所对应的充满Julia集中定义一些几何尺寸 ,求出J 集的近似标度不变因子α ,定性说明了M J混沌分形图谱标度不变的特性· 同时 ,发现Mandelbrot集周期芽苞的Fibonacci序列的拓扑不变性 ,阐述了Fibonacci序列是通向混沌的又一途径 ,为更好地了解M J混沌分形图谱的结构奠定了理论基础·The characteristic parameters of M J chaos fractal images generated by the complex map z←z w+c were studied. A series of families of chaos-fractal images were generated by using the escape time algorithm. The distant between super attracting periodic points was computed by many computational mathematic experiments, and universal constant δ in the Mandelbrot sets was discovered. When some geometrical dimensions were defined in full Julia sets corresponding with super attracting periodic points in the Mandelbrot sets, approximate scaling invariable factor α was computed. Those qualitatively demonstrate scaling invariance of M J chaos fractal images. Furthermore, the topological invariance on the Fibonacci sequence of the periodic buds was discovered. The Fibonacci sequence is another way to the chaos.

关 键 词：逃逸时间算法 M-J混沌分形图谱 超吸引周期点 普适常数 标度因子 FIBONACCI序列 MANDELBROT集 标度不变性 计算机数学 

分 类 号：O174.5[理学—数学] O415.5[理学—基础数学]