Abstract: In the research of fractal cities, the fractal dimension is very important. It is used to describe the fractal character of the city. The authors design two ways to calculate the fractal dimension by the box counting method through an example of Beijing, which are called the vector method and the grid method respectively. The former calculates the fractal dimension through an intersecting analysis in ArcView; and the latter is carried out by programming in Matlab. They are compared from three aspects: the calculating process, the limits in use and the results. As a result,they get the conclusion that there are merits and faults on both methods and they should be chosen to use properly in practical situation.

Key words: fractal dimension, box counting method, urban form, Beijing, remote sensing, GIS, Matlab

摘要： 在城市的分形研究中，常会计算其分维数，用分维数刻画城市的分形特征。作者以计算北京城市形态的分维数为例，介绍2种用网格法计算分维的方法：矢量法和栅格法。矢量法是在ArcView平台下通过叠加分析完成的，栅格法则是在Matlab环境下编程实现的。文章还将从实现过程、适用程度和计算结果3个方面对这2种方法作比较，得到的结论为矢量法和栅格法各有长短，各有适用场合。在具体的应用中，应根据实际情况选择合适的方法。?

关键词: 分维数, 网格法, 城市形态, 北京, 遥感, GIS, Matlab