A common feature of the mammalian striate cortex is the arrangement of 'orientation domains' containing neurons preferring similar stimulus orientations. They are arranged as spokes of a pinwheel that converge at singularities known as 'pinwheel centers'. We propose that a cortical network of feedforward and intracortical lateral connections elaborates a full set of optimum orientations from geniculate inputs that show a bias to stimulus orientation and form a set of two or a small number of 'Cartesian' coordinates. Because each geniculate afferent carries signals only from one eye and its receptive field (RF) is either ON or OFF center, the network constructs also ocular dominance columns and a quasi-segregation of ON and OFF responses across the horizontal extent of the striate cortex.