Tile rewriting grammars and picture languages

Tile rewriting grammars (TRG) are a new model for defining picture languages. A rewriting rule changes a homogeneous rectangular subpicture into an isometric one tiled with specified tiles. Derivation and language generation with TRG rules are similar to context-free grammars. A normal form and some closure properties are presented. We prove this model has greater generative capacity than the tiling systems of Giammarresi and Restivo and the grammars of Matz, another generalization of context-free string grammars to 2D. Examples are shown for pictures made by nested frames and spirals.