Spontaneous symmetry breaking and the formation of columnar structures in the primary visual cortex

Abstract

We presents a simple model in which the formation of ocular dominance columns in striate cortex emerges spontaneously. The model generalizes Kohonen's original self-organizing model while incorporating a continuous variable corresponding to ocularity. We demonstrates in this model that the column formation is a sort of phase transition due to (local) spontaneous breaking of left-right ocular symmetry in the distribution of nerve cells in the cortex observed at early stage. In particular, he derives an exactly (locally) periodic columnar structure with the hyper column width given by ∼4√3σ where σ is the lateral correlation length of the model. This result does not depend on the details of the generalization of Kohonen's model. Generalization to formations of another columnar structure is straightforward.