A Fractal Geometry Approach to Quantifying Aesthetic Values in Scientific Codes

Although the literature on programming style is large, sensori-emotional or aesthetic expression in code remains poorly understood empirically. In this paper, we study “beauty”-the measure of programming style-in code using the beauty factor, a simple, relativistic model of source beauty based on fractal geometry. What is new is we study beauty in eight popular scientific libraries of approximately two million lines of code which, individually or as a composite, have never been analyzed previously for programming style. What is furthermore new is we use these libraries as independent tests of the beauty hypothesis, namely, the viability of beauty factors as quantifiable code aesthetic. Using the eight libraries and 11 different semantic-preserving transformations, i.e., 88 experiments of 5,600 trials, the data indicates statistically significant patterns (P<;10
^-9
) consistent with previous studies of beauty factors on non-scientific, system codes. The data furthermore suggests evidence of statistically significant patterns (P<;10
^-32
) in which the beauty model also serves as a novel metric for estimating the mnemonicity of code. These conclusions have potential to inform certain long-held, deeply felt, and passionately argued beliefs and convictions about style that have guided both pedagogy and industry best practices.