Parallel and sequential specification of a context sensitive language for straight lines on grids

A context sensitive language over {0, 1} + is described whose words represent straight lines in the plane. Various generation and recognition algorithms for it are described. Affine transformations correspond to simple string rewriting algorithms. Motivating geometrical and number-theoretical aspects of linear geometry leading to the codes are indicated. The results are of interest for pattern recognition, computer graphics, parallel computation, and neural net theory.