分形维数(Fractal dimension)及其测量方法

Fractal Dimension and Its Metrical Methods

给出了相似维数、容量维数、盒子维数、信息维数、关联维数、广义维数分形维数等 6种分形维数的定义方式 ,并讨论了它们的应用范围。在此基础上 ,概括出改变粗视化程度求维数、根据测度关系求维数、根据关联函数求维数、根据分布函数求维数、根据波谱求维数等 5种测量维数的方法 ,为不同领域的科研人员应用维数测量提供了有力工具。

The definitions of six kinds of fractal dimension are introduced, including similarity of dimensions, capacity dimension, box dimension, information dimension, interrelation dimension and broad dimension, and their scopes of application are also discussed. On the basis of which five methods of measuring dimension are summed up in terms of megascopic degree, estimation, interrelation function, distribution function and spectrum function. This research provides a powerful tool for researching staff from different fields in dimension measurement.