Two exercises in formal composition

Spatial relations and shape grammars are defined. A spatial relation is specified by a finite number of shapes arranged in a certain way. A shape grammar provides for the recursive generation of arrangements of shapes in terms of given spatial relations. The possible spatial relations between two edge-connected polygons are characterised. The use of these spatial relations to define shape grammars generating distinct languages of shapes is discussed. The construction of shape grammars to generate infinite languages of shapes containing a given shape made up of polygons is also considered.