A diffuser language: Designing quadratic residue diffuser arrays with shape grammars

Abstract

This paper presents research on a rule-based approach to designing creative acoustic diffuser arrays. A shape grammar-influenced design method is specified that uses shape rules to recursively design arrays of quadratic residue diffusers (QRD) in a way that is neither mechanical nor deterministic. Shape grammar-based generative systems have already been shown to be capable of being used in architecture and engineering to create languages of functional objects but have not yet been extended into the realm of acoustics. The grammar presented by this paper produces a QRD-based acoustic diffusion language that breaks habits in QRD deploying techniques, which is lacking outside of using known equations that give known forms. The grammar can include different design frequencies and open the possibilities of different and non-uniform, intentional diffusion treatment. This paper will specify and demonstrate the formation rules, and discuss on how in combination with material specifications, this design method can generate broadband QRD arrays that address both performative and aesthetic criteria in new and surprising ways.