Generated designs are formed through rules that change, and structures that interpret, descriptions. The structure of design descriptions is examined with particular reference to generative shape descriptions acting as the infrastructure for attributes. Structure is represented by relations among the parts of descriptions. In particular, a closure structure allows relations to be described by the parts themselves. Design processes use descriptions in combination. It is shown how to combine separate descriptions in parallel and sequentially. Rules change descriptions. It is shown how to aggregate local changes consistently across a design and to use rules with structure on their component shapes to highlight selected emergent features. Further, multiple attribute descriptions, including shape and associated properties, are constructed. Their structures are represented algebraically.