Fractal geometry of literature: first attempt to Shakespeare's works

TL;DR

This study applies fractal geometry to analyze William Shakespeare's works, revealing geometric patterns and introducing new concepts like Zipf's dimension, with findings showing correlations between fractal measures and manuscript length.

Contribution

It is the first application of fractal geometry to literature analysis, proposing a novel method for calculating fractal dimensions of texts and introducing Zipf's dimension and Zipf's order.

Findings

Fractal dimensions correlate with manuscript length.

Zipf's law applies to letters, not just words.

Power-law relationships are observed in the data.

Abstract

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.