The Construction of Shapes

An algorithm for shape rule application is presented. A shape rule α → β applies to a labelled shape γ whenever there is a transformation τ that makes α a subshape of γ. In this case, a new labelled shape can be obtained by replacing the occurrence of τ(α) in 7 with τ(β). The algorithm required for this process is developed in this paper. This algorithm determines all possible distinct transformations under which a given shape rule applies to a given labelled shape and the corresponding labelled shapes resulting from such applications. The definitions and notations given for labelled shapes and shape grammars by Stiny (1980) are used.