The visual cortex as a crystal

A theory of pattern formation in primary visual cortex (V1) is presented that takes into account its crystalline–like structure. The cortex is partitioned into fundamental domains or hypercolumns of a lattice describing the distribution of singularities or pinwheels in the orientation preference map. Each hypercolumn is modelled as a network of orientation and spatial frequency selective cells organized around a pair of pinwheels, which are associated with high and low spatial frequency domains respectively. The network topology of the hypercolumn is taken to be a sphere with the pinwheels located at the poles of the sphere. Interactions between hypercolumns are mediated by anisotropic long range lateral connections that link cells with similar feature preferences. Using weakly nonlinear analysis we investigate the spontaneous formation of cortical activity patterns through the simultaneous breaking of an internal O(3) symmetry and a discrete lattice symmetry. The resulting patterns are characterized by states in which each hypercolumn exhibits a tuned response to both orientation and spatial frequency, and the distribution of optimal responses across hypercolumns is doubly periodic or quasi–periodic with respect to the underlying lattic