A computational model is proposed for some general aspects of information flow in the visual cortex. The basic process, called “sequence seeking,” is a search for a sequence of mappings, or transformations, linking source and target patterns. The process has two main characteristics: it is bidirectional, bottom-up as well as top-down, and it explores in parallel a large number of alternative sequences. This operation is performed in a “counter streams” structure, in which multiple sequences are explored along two complementary pathways, an ascending and a descending one, seeking to meet. A biological embodiment of this model in cortical circuitry is proposed. The model serves to account for known aspects of cortical interconnections and to derive new predictions.