Fractal geometry of texts: An initial application to the works of Shakespeare

Abstract

It has been demonstrated that there is a geometrical order in text structures. Fractal geometry, as a modern mathematical approach and a new geometrical standpoint on natural objects including both processes and structures, is here employed for textual analysis. For this first study, the works of William Shakespeare were chosen as the most important items in Western literature. By counting the number of letters in a text, it is possible to study the whole text statistically. A novel method based on basic assumption of fractal geometry is proposed for the calculation of fractal dimensions of texts. The results are compared with Zipf's law. Zipf's law is successfully used for letters instead of words. Two new concepts – namely Zipf's dimension and Zipf's order – are also introduced. It can be seen that changes of both fractal dimension and Zipf's dimension are similar, and dependent on the text length. Interestingly, directly plotting the data obtained in semi-logarithmic and logarithmic forms also leads to a power-law.