The visual cortex of many adult mammals has patches of cells that receive inputs driven by the right eye alternating with patches that receive inputs driven by the left eye. These ocular dominance patches (or ``columns'') form during early life as a consequence of competition between the activity patterns of the two eyes. A mathematical model of several biological mechanisms that can account for this development is presented. Analysis of this model reveals the conditions under which ocular dominance segregation will occur and determines the resulting patch width. Simulations of the model also exhibit other phenomena associated with early visual development, such as topographic refinement of cortical receptive fields, the confinement of input cell connections to patches, monocular deprivation plasticity including a critical period, and the effect of artificially induced strabismus. The model can be used to predict the results of proposed experiments and to discriminate among various mechanisms of plasticity.