Universality in visual cortical pattern formation

During ontogenetic development, the visual cortical circuitry is remodeled by activity-dependent mechanisms of synaptic plasticity. From a dynamical systems perspective this is a process of dynamic pattern formation. The emerging cortical network supports functional activity patterns that are used to guide the further improvement of the network's structure. In this picture, spontaneous symmetry breaking in the developmental dynamics of the cortical network underlies the emergence of cortical selectivities such as orientation preference. Here universal properties of this process depending only on basic biological symmetries of the cortical network are analyzed. In particular, we discuss the description of the development of orientation preference columns in terms of a dynamics of abstract order parameter fields, connect this description to the theory of Gaussian random fields, and show how the theory of Gaussian random fields can be used to obtain quantitative information on the generation and motion of pinwheels, in the two dimensional pattern of visual cortical orientation columns.