汉字的分形性及其计盒维数的统计分析

Fractal Analysis of Chinese Characters and the Calculation of its Box-Counting Dimension

本文首次把分形理论用于研究汉字，实验显示出汉字具有分形特性———标度不变性，在此基础上，本文对国标一级字库３７５５个汉字的分形维数———计盒维数进行了计算统计，得到了其统计分布规律。实验结果表明：计盒维数较好地反映了汉字笔划、结构的繁杂程度和不规则性，这些新的发现表明将分形理论用于汉字信息处理（识别、压缩、笔迹鉴别等）具有巨大的潜力和应用前景。

In this paper,we succeeded in applying fractal theory to the analysis of Chinese characters for the first time .First,we found that Chinese characters are invariant to different scales ,thus ,from the point of geometry,Chinese characters could be regarded as one kind of fractal.Then,we calculated the box-counting dimension of the whole 3755 Chinese characters in National Standard Chinese Character Set I and obtained the fractal dimension distribution,from which a conclution was that box-counting dimension could depict the complexity and irregularity of Chinese Characters' strokes and structure.The preliminary results suggest that using fractal theory in Chinese information processing appears to hold promise.