分形维数计算方法的研究  

Fractal Dimension Study of Calculating Method

作　　者：聂笃宪[1] 曾文曲[1] 文有为[1] 

机构地区：[1]广东工业大学计算机学院,广东广州510090

出　　处：《微机发展》2004年第9期17-19,22,共4页Microcomputer Development

基　　金：广东省基金资助项目((2003)32475)

摘　　要：分形维数作为科学研究的重要工具之一,它是描述自然界和非线性系统中不光滑和不规则几何体的有效工具,其计算方法已经有多种,应用领域也是十分广泛。然而,各种方法各有不同,文中就此对常用分形维数计算方法进行了系统的综合与研究,主要包括圆规法、明科斯基方法、变换方法、盒子计算方法、周长-面积法、裂缝岛屿方法、分形布朗模型法,对每种方法的含义和模型及相关的应用领域进行了阐述,并给出了其方法的计算机实现算法。As one of science study tools,fractal dimension is usually an effective way that used to describe the non-smooth and non-regular geometry objects in the nature and non-linear systems.There are all kinds of methods about calculating it.Its application is greatly wide,but there are distinctive differences between these methods. According to these, this paper studies and integrates these methods systematically,including Compass Method,Minkowski Method,Variation Method,Box counting Method,Perimeter Area Method,Slit island Method,Fractal Brown model Method.This paper also expatiated the meanings,basic models and the application in each field.At the same time,algorithms of these methods implemented by the computer are found in the paper.

关 键 词：分形维数 分形几何学 计算方法 非线性系统 

分 类 号：O415.5[理学—理论物理]