Shape grammars were first introduced in a seminal article by George Stiny and James Gips in 1971.
These publications also contain two independent, though equivalent, constructions showing that shape grammars can simulate Turing machines.
A shape grammar system additionally has a working area where the created geometry is displayed.
If there are several matches, the engine can (depending on its configuration/implementation) Shape grammars are most useful when confined to a small, well-defined generation problem such as housing layouts and structure refinement.
The palladian villas shape grammar presented by William Mitchell[2] for example contains 69 rules, that are applied throughout eight stages.
This typically affects internal proportions of the new shape so that a greater variety of forms can be created.
Other important domains shape grammars have been applied in are decorative arts, industrial design and engineering.