this paper makes use of a particular sort of similarity transformations called grid transformations. The results concern language theoretic aspects and algorithmic properties of context-free collage languages and of patterns generated by iterated function systems, where the generating devices use only grid transformations. It turns out that the language classes have nice closure properties, and that non-trivial questions concerning the generated pictures can be decided. These studies extend the results of [Dre96a], where it is shown 1