可数无穷多极值点复映射族计算机图形化研究  

RESEARCH ON VISUAL PRESENTATION OF COMPLEX MAPPING FAMILY WITH COUNTABLY INFINITE CRITICAL POINTS USING COMPUTER

作　　者：陈宁[1] 朱晓玲[1] 

机构地区：[1]沈阳建筑工程学院计算机科学与工程系,沈阳110015

出　　处：《计算机研究与发展》2001年第12期1512-1519,共8页Journal of Computer Research and Development

基　　金：国家自然科学基金 ( 6 99730 33);教育部2000年"高等学校骨干教师资助计划"基金;辽宁省自然科学基金 ( 9810 2 0 0 10 6 );辽宁省教委基金 ( 2 0 2 0 2 2 5 9);沈阳市科委基金 ( 2 0 0 14 13-0 1)资助

摘　　要：用超越复映射 F(z) =ezw+c构造出含有单参数 w(w≠ 0或 1)的牛顿变换族 fw(z) =z- 1wzw- 1 模型 ,fw(z)有可数无穷多个极值点 .提出了构造参数 w的有效极值点集 vcps={ zk|-π<arg(zk)≤π,f′w(zk) =0 ,k∈ Z ,zk∈C }方法 ,用参数平面上 vcps中所有极值点的轨道有界的参数 w构造了 fw(z)的广义 M集 ,同时用参数平面上 vcps中第 n个极值点的轨道有界的参数 w构造了 fw(z)的 MF,MS和 MO广义 M集 .分析了不同的参数下 fw(z)的动力学特性 ,根据动力平面上点的轨道被参数 w极值点的吸引轨道的吸引时间 ,构造了大量的新颖的充满 J集图像 .Newton's transformation family f w(z)=z-1wz w-1 containing only one complex parameter w(w≠0 or 1) is constructed from the transcendental mapping z→e z w+c . The number of the critical point of f w(z) is countably infinite, and a method ( vcps ) is presented to generate the valid critical point set about the parameter w , vcps = {z k|- π < arg (z k)≤ π , f ′ w(z k)=0, k∈ Z , z k∈ C}. The Mandelbrot (M) set of f w(z) is constructed according to the w in the parameter plane, about which the orbits of all of the critical points in the vcps are bounded.The other generalized M sets of f w(z) , such as M F, M S, M O and so on, are constructed from the parameter w , in whose vcps the orbit of the n th critical point is bounded. The dynamical characters of f w(z) of the different parameter are analyzed. A great number of novel images of filled-in Julia sets are generated based on the attracting time in which the orbit of a point in the dynamical plane is attracted to the orbit of a critical point of the parameter w .

关 键 词：混沌 分形 牛顿变换 M集 J集 计算机图形化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]