Neurons within a cortical macrocolumn can be represented in continuum state equations that include axonal and dendritic delays, synaptic densities, adaptation and distribution of AMPA, NMDA and GABA postsynaptic receptors, and back-propagation of action potentials in the dendritic tree. Parameter values are independently specified from physiological data. In numerical simulations, synchronous oscillation and gamma activity are reproduced and a mechanism for self-regulation of cortical gamma is demonstrated. Properties of synchronous fields observed in the simulations are then applied in a model of the self-organization of synapses, using a simple Hebbian learning rule with decay. The patterns of connection of maximally stable configuration are compared to real cortical synaptic connections that emerge in neurodevelopment.