分形维数计算方法研究进展

Review on methods of calculating fractal dimension.

分形理论作为描述自然界和非线性系统中不光滑和不规则几何形体的有效工具 ,如何将其应用到林学与水土保持等学科中去 ,是目前学术界正在研究的热点问题 .为此 ,该文在对分形理论进行概述的基础上 ,列举了描述分形维数的一般形式及计算分形维数的主要方法 ,包括标尺法、半方差法、PSD法 ,以及根据测度关系、相关函数、分布函数等方法求分维 .对每一种方法的含义、基本模型及在相关领域的应用进行了阐述 。

As an effective way to describe the non smooth and non regular geometry objects in the nature and non linear systems,fractal theory has been applied to many fields. On the basis of summarizing the fractal theory,this paper listed the common forms of describing fractal dimension as well as the methods of calculating it,including staff guage method,semivariance method,particle size distribution(PSD) method and the methods of counting it by measuring relation, correlated function and distribution function. This paper also expatiated the meanings,basic models and the application in each field of each method. At last, the prospect of fractal theory is briefly appraised.