IFS拓扑不动点原理构造混沌分形图的研究  

Research on Constructing Chaos-Fractal Images Based on IFS Attractor

作　　者：付冲[1] 马希敏[2] 陈英[2] 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 [2]辽宁经济职业技术学院计算机系,辽宁沈阳110036

出　　处：《工程图学学报》2006年第3期125-129,共5页Journal of Engineering Graphics

基　　金：教育部博士学科点专项科研基金资助项目(20030145030);辽宁省自然科学基金资助项目(20042020)

摘　　要：分形学是一种描述自然界中广泛存在的具有自相似结构的非线性复杂系统内部规律的理论,迭代函数系统(IFS)是构造分形集的核心技术。研究了各类基于IFS吸引子的混沌分形图的计算机构造方法;分析了其应用范围和局限性,对构造混沌分形图的确定性算法、随机迭代算法、字符串替换法、逃逸时间算法和反函数迭代法进行了深入的探讨和对比分析;总结了混沌分形图构造的基本规律。并首次用Java语言实现了各种算法,给出了几种较为常用算法的迭代参数、公式及实验结果。Fractal is the theory of describing the inner rules of the nonlinear complex systems with self-similar structure that widely exists in the nature and IFS is the key technology of constructing fractal images. In this paper, various computer construction algorithms of generating chaos-fractal images based on IFS attractor are studied and their application range and limitation are analyzed. The determination algorithm, Iterated Function System with Probability algorithm, string substitution algorithm, escape time algorithm and inverse function iterating algorithm are thoroughly compared and discussed and the basic rules of constructing chaos-fractal images are concluded. The iteration arguments, expression and the chaos-fractal images that implemented by Java are also given.

关 键 词：计算机应用 混沌分形图 迭代函数系统吸引子 不动点原理 仿射函数 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]