COLLAGE GRAMMARS

In this paper, we introduce and study the notion of collage grammars. A collage (in our sense) consists essentially of a set of parts being geometric objects and a set of hyperedges being subjects of further replacement. A set of collages represents a set of geometric patterns where each pattern is just the union of the parts of a collage. By overlay of the represented patterns, a set of collages yields a fractal pattern. Finally, collage grammars embody syntactic means for the generation of sets of collages in the usual way. As collages represent patterns that may be overlaid in addition, collage grammars provide also syntactic devices for the generation of sets of patterns as well as a certain type of fractal patterns.