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.