Research on the Vector Box-counting Algorithm in Fractal Dimension Measurement
测量分维的矢量计盒算法研究

The fractal theory developed by the French scientist Mandelbort in 1970s is beneficial in many areas.It greatly expands and deepens our knowledge on irregular geometric bodies.Fractal theory quantifies these phenomena mainly by ascertaining their fractal dimensions.Box-counting algorithm is the one most practical and also most frequently adopted method.The traditional box-counting algorithm is based on the grid document and has some serious shortcomings,such as the distortion of the image being enlarged,the trivialness of the process and the finite of the iterative degree,etc.The vector box counting algorithm developed in this paper takes vector document as the carrier and has three advantages.First,the image will not be distorted after being enlarged.Second,the process is completely handled by computer,simple and reliable.Third,to some degree,the iterative degree can be infinite.Therefore,it can ascertain precisely the scaling space of the graph and acquire accurate fractional dimension value.This paper expounds the data structures,the process of disposing and the main functions in detail.What's more,it proves the precision and advantages of the vector box counting algorithm by making use of Koch curve,osteoma boundary and river system.The result shows that the vector box counting algorithm is a convenient,useful and precise way of dimensional calculating method.