Parallel Generation of Finite Images

We define a syntactic model for generating sets of images, where an image can be viewed as an array over finite alphabet. This model is called image grammar. Image grammar can be considered as a generalization of classical Chomsky grammar. Then we study some combinatorial and language theoretical properties such as reduction, pumping lemmas, complexity measure, we give a strict infinite hierarchy. We also characterize these families in terms of deterministic substitutions and Chomsky languages.