Beautiful 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 Birkhoff’s 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. Additionally, there were certain patterns that both experienced and non-experienced participants agreed on. Our findings suggest that Birkhoff’s aesthetic measure reveals useful aesthetic information of trochoid patterns.