复映射z←sinz^2+c的广义M-J混沌分形图谱  

Research on Chaos-Fractal Images Constructed by Complex Mapping z←sinz^2+c

作　　者：付冲[1] 王培荣[1] 徐吉吉 朱伟勇[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2004年第10期950-953,共4页Journal of Northeastern University(Natural Science)

基　　金：教育部博士学科点专项科研基金资助项目(200014512);国家自然科学基金资助项目(69974008).

摘　　要：推广了由多项式函数族构造的M J混沌分形系统,研究了复映射z←sinz2+c所构造的广义M集和J集,利用逃逸时间算法绘制了M集和J集的混沌分形图·通过大量计算机数学实验,找到了M集各主要周期芽苞的分布规律,并与具有典型意义的复映射z←z2+c所构造的M集进行了对比分析,指出了两者之间的异同·发现了复映射z←sinz2+c的广义J集的非连通特殊性,分析了图谱构成及周期点位置,指出其具有无穷嵌套、自相似的分形结构·通过研究各周期芽苞内的点所对应的J集分形图,得出了广义M集周期芽苞内点的周期数与相应J集吸引周期轨道周期数相等的结论,并讨论了M集与J集之间的对应关系·The M-J chaos-fractal system constructed by polynomial function sets was extended to studying the generalized M set and J set, which are constructed by complex mapping z←sinz^2+c, so as to plot the chaos-fractal images of M and J sets by use of escape time algorithm. The distribution rules of main periodic buds in M set were found by lots of computer mathematic experiments and compared with the M set constructed by the typical complex mapping z←z^2+c, thus revealing the differences between them. It was found that the generalized J set constructed by complex mapping z←sinz^2+c is characterized by discontinuity. The image structure and position of periodic point were analyzed, from which a conclusion could be drawn that it has an infinitely embedded and self-similar fractal construction. The study on J set fractal image corresponding to the point in each periodic bud reached a conclusion that the number of periods of a point in a periodic bud of M set equals to that of the periodic attraction orbit of corresponding J set. The relationship between M set and J set were also discussed.

关 键 词：混沌分形图 MANDELBROT集 JULIA集 逃逸时间算法 周期芽苞 周期轨道 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]