基于三维盒维数算法的城市分维计算

计算机应用 ›› 2010, Vol. 30 ›› Issue (8): 2070-2072.

基于三维盒维数算法的城市分维计算

张乐珊¹,陈戈²,韩勇³,张涛³

1. 中国海洋大学
2. 中国海洋大学信息工程学院海洋技术系
3.

收稿日期:2010-01-26 修回日期:2010-03-16 发布日期:2010-07-30 出版日期:2010-08-01
通讯作者: 张乐珊

3D box-counting algorithm for calculating fractal dimension of cities

Received:2010-01-26 Revised:2010-03-16 Online:2010-07-30 Published:2010-08-01

摘要/Abstract

摘要： 通过将传统的二维盒维数算法扩展到三维空间，提出了一个基于三维空间的盒维数计算方法。分别利用三维盒维数算法和二维盒维数算法计算城市的分维，通过对计算结果进行比较分析，观察到城市空间结构在第三维同样具有分形特征，证明传统城市分维计算中采用基于二维空间的分维算法或者简单地利用二维分维加1的方法表示三维分维都是不准确的，并进而给出正确的城市分维计算方法。

关键词: 三维盒维数, 分形维度, 城市分形

Abstract: The traditional 2D box-counting fractal dimension algorithm has been extended to the 3D space, and a 3D-based box-counting fractal dimension algorithm was proposed. And, the 2D and 3D algorithm were used respectively to study the fractal characters of city. Through comparing the results, the fractal character of the spatial structure of cities along the third dimension was observed, proving that the traditional fractal cities study based on two dimensional fractal dimension algorithm, or simply adding "1" to the 2D fractal dimension to represent the 3D fractal dimension were not correct, furthermore, the correct method used in fractal city study was put forward.

Key words: 3D box-counting fractal dimension, fractal dimension, fractal city

张乐珊陈戈韩勇张涛. 基于三维盒维数算法的城市分维计算[J]. 计算机应用, 2010, 30(8): 2070-2072.