Shapes, structures and shape grammar implementation. (June 2019) - Jowers, Iestyn
Abstract: 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 shape 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 implications of this result for shape grammar implementation and for design descriptions in CAD. Highlights: A series of simple shape grammars are analysed according to fixed part strucutres. It is shown that symmetric embedded lines result in periodic palindromic structures. It is shown that these structures can limit the application of shape rules. Implications for shape grammar implementation, and CAD in general, are discussed.