文学的分形几何：莎士比亚作品初探
Fractal geometry of literature: first attempt to Shakespeare's works
摘要：
论证了文学结构中存在着一种几何秩序。分形几何作为一种现代数学方法和一种新的几何观点，包括过程和结构的自然对象被用来分析文献。作为第一个研究，威廉·莎士比亚的作品被选为西方文学中最重要的项目。通过计算手稿中应用的字母数量，可以对整个手稿进行统计研究。基于分形几何的基本假设，提出了一种计算分形维数的新方法。并与Zipf定律进行了比较。齐普夫定律成功地用于字母而不是单词。引入了Zipf维数和Zipf阶两个新概念。研究发现，分形维数和Zipf维数的变化规律相似，且都依赖于原稿长度。有趣的是，直接绘制半对数和对数形式的数据也导致了幂律。
英文摘要：
It was demonstrated that there is a geometrical order in the structure of literature. Fractal geometry as a modern mathematical approach and a new geometrical viewpoint on natural objects including both processes and structures was employed for analysis of literature. As the first study, the works of William Shakespeare were chosen as the most important items in western literature. By counting the number of letters applied in a manuscript, it is possible to study the whole manuscript statistically. A novel method based on basic assumption of fractal geometry was proposed for the calculation of fractal dimensions of the literature. The results were compared with Zipf's law. Zipf's law was successfully used for letters instead of words. Two new concepts namely Zipf's dimension and Zipf's order were also introduced. It was found that changes of both fractal dimension and Zipf's dimension are similar and dependent on the manuscript length. Interestingly, direct plotting the data obtained in semi-logarithmic and logarithmic forms also led to a power-law.
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