一个非解析复映射的广义Mandelbrot集  

Generalized Mandelbrot sets from a nonanalytic complex mapping

作　　者：王兴元[1] 骆超[1] 

机构地区：[1]大连理工大学电子与信息工程学院,辽宁大连116024

出　　处：《大连理工大学学报》2009年第1期128-132,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(60573172);高等学校博士学科点专项科研基金资助项目(20070141014);辽宁省自然科学基金资助项目(20082165)

摘　　要：推广了Michelitsch等所提出的由一个简单非解析映射构造Mandelbrot集的方法,并由推广的复映射,构造出一系列实数阶的广义Mandelbrot集(简称广义M集).利用复变函数理论和计算机制图相结合的实验数学方法,对广义M集的结构和演化进行了研究.结果表明:广义M集的几何结构依赖于参数α和R;整数阶广义M集具有对称性和分形特征;小数阶广义M集出现了错动和断裂,且其演化过程依赖于相角主值范围的选取.The method constructing the Mandelbrot sets from a simple nonanalytic mapping developed by Michelitsch, et al. was expanded. According to the expanded complex mapping, a series of the generalized Mandelbrot sets for real index number were constructed. Using the experimental mathematical method combining the theory of analytic function of one complex variable with computer-aided drawing, the fractal features and evolutions of the generalized Mandelbrot sets were studied. The results show the following facts： the geometry structure of the generalized Mandelbrot sets depends on the parameters of α and R; the generalized Mandelbrot sets for integer index number have symmetry and fractal feature; the generalized Mandelbrot sets for decimal index number have discontinuity and collapse, and their evolutions depend on the choice of the principal range of the phase angle.

关 键 词：非解析映射 广义M集 分形 演化 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]