广义M-J集的边界构造及分维数计算  

Construction Method in the Edge of General M-J Sets and its Fractal Dimension

作　　者：章立亮[1] 

机构地区：[1]宁德师范高等专科学校数学研究所,福建宁德352100

出　　处：《小型微型计算机系统》2008年第7期1338-1342,共5页Journal of Chinese Computer Systems

基　　金：福建省自然科学基金项目(Z0511053)资助

摘　　要：讨论逃逸时间算法、Lyapunov指数法、反函数法和同胚分形插值法等方法的适用范围,提出构造广义M-J集分形边界的一种通用算法即边界检测算法.利用设计的检测模板将广义M-J集的边界部分提取出来并计算这种分形边界的盒维数.实验结果表明,与几种现有的算法相比较,新算法具有普适性和精确性,用于构造任意形式复映射的广义M-J集的分形边界.The fraetal edge of general M-J set and Its fractal dimension are studied. The properties of escape time algorithm, Lyapunov exponent algorithmand inverse function algorithm are analyzed. The algorithm based on edge detection is put forward to build the edge of general M-J set and box dimension of fractal edge are calculated. The experimental result show that both universal and high definition can be acquired with the new algorithm. The new algorithm can be used to building of the fractal edge for general M-J sets.

关 键 词：MANDELBROT集 JULIA集 分形 边界检测 盒维数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]