Shape grammars are a computational system that generates geometric shapes through production rules, functioning as a way to study 2D and 3D languages. George Stiny and James Gips introduced shape grammars in their 1971 seminal paper, establishing them as a specific class of production systems that can simulate Turing machines. The mathematical foundations were developed in Stiny's 1975 book, while Gips explored applications in his 1975 publication.

A shape grammar consists of shape rules with left-hand and right-hand sides separated by an arrow, plus a generation engine that processes these rules. The system includes a start rule, transformation rules, and a termination rule, with markers helping to locate and orient new shapes. Unlike Chomsky grammars, shape grammars can apply rules in parallel or serial fashion, similar to L-systems. The generation engine searches the current working shape for matches to rule conditions, choosing which rules to apply based on configuration.

Despite academic popularity in architecture, decorative arts, industrial design, and engineering, shape grammars haven't achieved widespread use in generic CAD applications. The most practical applications occur in constrained problems like housing layouts and structure refinement. Notable implementations include the Palladian villas grammar with 69 rules across eight stages, and parametric extensions that allow shapes to respond to structural conditions like beam widths based on span requirements.