负整数次幂复解析映射构造分形

发布时间：2018-06-19 09:10

本文选题：分形 + 迭代函数系　；参考：《小型微型计算机系统》2017年09期

【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.
[Abstract]:In order to construct a new fractal of the family of negative integer power complex mappings, the method of constructing a nonlinear iterative function system by using the 1-period parameters of the generalized M set of the complex mapping family is studied. According to the symmetry of the generalized M set, the parameter region of the M set at the angle of 蟺 / n 1 is selected as the parameter source region of the compressed iterative function in constructing IFSIterated function systems (function iterations). Two or more parameters are selected to construct the nonlinear compression IFSs and the fractal is constructed. According to the symmetry characteristic of the 1-cycle parameter region of the complete M set, several parameters are selected in the parameter source region, and each parameter is extended to n 1 rotational symmetric parameter or 2 n 1) rotational symmetry parameter and reflection symmetry parameter. The corresponding iterative functions are constructed from these parameters to form a nonlinear IFS and a symmetric fractal is constructed. The experimental results show that the nonlinear IFSs constructed by the present method can be used to construct a large number of novel fractals with different structures using the complex mapping family fznnc.
【作者单位】：沈阳建筑大学信息与控制工程学院;
【基金】：国家自然科学基金项目(61272253)资助
【分类号】：O174

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