We present two related computational models of ocular dominance column formation. Both address nervous system plasticity in terms of sprouting and retraction of axonal processes rather than changes in synaptic strength implied by synapse-specific Hebbian models. We employ statistical mechanics to simulate changes in the pattern of network connectivity. Our formalism uses the concept of an energy function, which we interpret as related to the levels of target-generated neurotrophins for which afferents compete. In contrast, synapse-specific Hebbian models impose synaptic normalization, for which there is little experimental evidence, in order to induce competition. Our models make many predictions which require experimental investigation. We suggest that the absence of monocular deprivation effects in the optic tectum may be due to a tendency of amphibian retinal ganglion cells to preserve the complexity of their terminal arbors. One model raises the possibility that boundaries separating columns in the mammalian cortex are poorly innervated if they have been formed by complete but asynchronous retinal activation. Both models exhibit a phase transition, suggesting a discontinuity in the transition from a binocular cortex to one possessing ocular dominance columns. Finally, our other model could account for the perpendicularity of ocular dominance columns to the boundary of the primary visual cortex while admitting of less ordered central patterns.