Shapes, structures and shape grammar implementation

Shape grammars are a generative formalism in which dynamic changes to shape structure plays a vital role. Such changes support ambiguity and emergence, and as a result shape grammars are often used as the basis for proposed developments in supporting shape exploration in computer-aided design. However, the general implementation of shape grammars remains an unsolved problem, and a common solution is to adopt a fixed structure. This paper explores the consequences of assuming a fixed structure, via analysis of a simple shape grammar, often used as a benchmark problem to illustrate advances in shape grammar implementation. With reference to the combinatorics of words, it is proved that adopting a finite fixed structure limits the capability of a shape grammar. The paper concludes with a discussion exploring the implication of this result for shape grammar implementation and for design descriptions in CAD