Explorations in using an Aperiodic Spatial Tiling as a Design Generator

Abstract

This paper describes the computational implementation of a three-dimensional, aperiodic spatial tiling for design generation. The mathematical spatial tiling formalism is related to the shape grammar formalism to illustrate commonalties between the two approaches to spatial design generation. Computational encoding of a mathematical tiling description as a basic grammar creates a generative design tool that can be used to study the visual properties of the spatial tiling and assess its potential for interesting use in design. The generative system is then relaxed by moving to an unrestricted grammar that expands the generative power to explore alternate design viewpoints and illustrate advantages of encoding a spatial tiling as a shape grammar. Potential design contexts for using the grammar presented include architectural spaces, structures and building façade patterns.