Fractals, Complexity Science, and the Visual Arts

This project strives to quantify ambiance in the visual arts with fractals, entropy, and complexity science techniques with the broad goal of bridging the gap between humanities and physics by finding meaningful mathematics to describe phenomena characteristic of the humanities and visual arts. The power of the arts is conveyed emotion and meaning as a construct from basic artistic features. Current research revolves around the use of neural networks to perform image analysis, which place an emphasis on the recognizable content of the image. This study focuses on quantifying artistic features such as color, hue, composition, and texture that are integral to the ambiance and meaning that a painting conveys. Relaying emotion in visual arts can be considered analogous to relaying information, which can be quantified by means of entropy. By experimenting with different microstate definitions, entropy calculations are adapted to include the color, composition, texture, and other defining features of paintings. Coupling entropy calculations with investigations of fractional dimensions creates unique methodology for mathematically quantifying the ambiance of a painting without forgoing the stylistic nuances that are the basis of the study and theory of art.