负整数次幂复解析映射构造分形  

Construction of Fractals from the Analytical Complex Mapping Family with Negative Integer Powers

作　　者：陈宁[1] 李明[1] 吴晓辰[1] 

机构地区：[1]沈阳建筑大学信息与控制工程学院,沈阳110168

出　　处：《小型微型计算机系统》2017年第9期2166-2170,共5页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61272253)资助

摘　　要：为构造出负整数次幂复映射族f(z)=z^(-n)+c的新型分形,研究了利用该复映射族的广义M集的1周期参数构造非线性迭代函数系的方法.根据广义M集的对称性,选定正实轴上方与正实轴成π/(n+1)角度内的M集中1周期参数区域为构造IFS(Iterated Function Systems,函数迭代系)中压缩迭代函数的参数源区域;试验选取2个或以上参数构造非线性压缩IFS,并构造分形.根据完整M集的1周期参数区域的对称特点,在参数源区域挑选多个参数,将每个参数扩展到n+1个旋转对称参数或2(n+1)个旋转对称和反射对称参数,由这些参数构造出相应的迭代函数,组成一个非线性的IFS,并构造出对称分形.实验结果表明,用本文方法构造的非线性IFS,可以用复映射族f(z)=z^(-n)+c构造出大量的结构各异的新颖分形.To construct the new style of fractals from the complex mappings of f（z）=z-n＋c with the negative integer powers,we research the method of how constructing nonlinear iterated function system with 1-periodic parameters in the generalized M set of the complex mapping.According to the symmetries of the generalized M set,we take the 1-period parameter regions,which are located between the radial line in the π/（n＋1）angle and the positive real axis,as the source parameter regions for construction of the iterated function systems （IFSs）.We choose Two or more parameters to construct the nonlinear IFSs,and generate their fractal.Based on the symmetries of the 1-periodic parameter region of the whole M set,we respectively expand the parameters in the source parameter regions into n＋1 rotational symmetric parameters（Zn＋1）or 2（n＋1） rotational symmetric and reflective symmetric parameters（Dn＋1）,we use the functions from these parameters to construct the nonlinear IFSs and then construct the symmetric fractals.The experimental results show that the nonlinear IFSs from the mapping family of f（z）=z^-n＋c can be used to construct a large number of novel fractals with the complex structures.

关 键 词：分形 迭代函数系 复映射 M集 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]