复映射z←z^(-2)+c广义M集倍周期芽苞标度性  

Mandelbrot Set's Multiplier Periodic Buds in Complex Mapping z←z^(-2)+c

作　　者：宋春林[1] 邓学工[1] 李志勇[1] 朱伟勇[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]东北大学计算中心,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2003年第4期330-333,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目 (699740 0 8);国家教育部博士学科点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 f(z,c) =z-2 +c所产生的广义M集 ,利用周期分类法绘制了广义M集的分形图 ,分析了M集周期芽苞及倍周期芽苞在主轴上同分岔图的对应关系·从分岔图入手 ,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符号序列的排列规律 ,给出了构造任意倍周期芽苞字提升方程的一个算法·利用二分法解字提升方程 ,得到主轴上各倍周期芽苞的超吸引点 ,发现M集倍周期芽苞在主轴上存在一个普适常数δ ,并在非主轴上进行了验证·深刻揭示了分形的自相似本质 。The general Mandelbrot set of complex mapping f(z,c)=z -2+c was studied. The general Mandelbrot set's fractal image was protracted with periodic classification method,and then the relationship between the Mandelbrot set's period-buds, multiplier periodic buds and bifurcation image was analyzed. The rule of symbol sequence on the super-attracted point was found when the multiplier periodic buds was on the principal axis by using of lots of experiments. A novel algorithm for constructing word-lifting formula of arbitrary multiplier periodic buds was presented. The super-attracted points of multiplier periodic buds on the principal axis were obtained by solving the word-lifting formula.There exists a general constant δ on the principal axis. The general constant δ was furthermore validated on the nonprincipal axis. The self-similar nature of fractal images was found.

关 键 词：M集 周期分类法 倍周期芽苞 分岔图 符号序列 字提升方程 标度因子 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]