Parameterized Shape Grammar for Generating n-fold Islamic Geometric Motifs

The complex formation of Islamic geometric Patterns (IGP) is one of the distinctive features in Islamic art and architecture. Many have attempted to reproduce these patterns in digital form, using various pattern generation techniques. Shape grammars are an effective pattern generation method, providing good aesthetic results. In this paper we present a novel approach in generating 3D IGP using an extended shape grammar: Parametrized Shape Grammar (PSG). PSG allows a user to generate both original and novel forms of Islamic geometric motifs (a repeated unit of a pattern). PSG is generalized to generate n-fold Islamic geometric motifs in a 3D environment, practically implemented as a 3D modeling tool within Autodesk Maya. The parametrization within each grammar rule is the key to generating numerous original and novel Islamic geometric motifs.