Quantifying aesthetic beauty through its dimensions: a case study on trochoids

Abstract

This paper examines the aesthetic dimensions of the patterns generated from trochoids. A virtual trochoid was implemented and its parameters were varied to generate various patterns. These patterns were evaluated by a group of 101 participants. Inspired by Birkhoffs concept of measuring aesthetics, order to complexity, we calculated order as the quality related to composition and complexity as the quality related to the intricacy of the structure. The result of this experiment suggests that the aesthetic measure was able to predict at least half of the preferred patterns by the participants and that those with art experience were more developed in considering a balanced composition. There were also certain patterns that both the experienced and non-experienced participants agreed on. This was further analysed using Arnheims theory of compositional weight, where size, colour, negative space and central perceptual force determines whether the trochoids had a sense of unity in its composition. To quantify these factors, the patterns ink density, ink distribution and ink gradient were measured. Our findings suggest that Birkhoffs aesthetic measure reveals useful aesthetic information of trochoid patterns and that patterns that are cohesive appears to be more appealing.