See also Grammatical inference.
In computer graphics these are also called “procedural representations”, or L-systems.
Prusinkiewicz and Lindenmayer (of “L-systems” fame) had success in describing plants and seashells and other CGI-friendly lifeforms as grammars. Lerdahl and Jackendoff applied these ideas to music. Look around for applications to primatology, genetic programming, gene expression, dynamical systems, Barnsley et al and their fractal image compression...
Design grammars are just ordinary grammars (possibly probablistic ones, but nevertheless...). Unlike classical the usual linguistic use of the word grammar”, though, the emphasis here is not simply on parsing sentences to see if they are valid or not, but rather using grammars to synthesisze entirely new sentences/flowers/trees/dungeons.
I should mention that I am interested in this for artistic/creative reasons rather than purely analytic ones.