We define a new methodology, aesthetic computing, for customizing discrete structures found in mathematics, programming, and computer simulation. The methodology is presented as a procedure, defined within the context of the semantic web, involving a successive chain of model transformations from a source model to a target model, with the source model being the discrete structure to represent and the target model being the geometric model. We also present an implementation based on this methodology, and a class where empirical studies were performed to assess student perceptions on how customized model structures affected their understanding and preferences regarding visual and interactive model representations. Students appear to prefer the methodology as a way to inject creativity into model building, and to allow them to explore alternative, analogical representations influenced by the fields of aesthetics and the arts.