In the vertebrate central nervous system, afferent axons find their appropriate target structures under the influence of local environmental cues. In many target regions, appropriate patterns of activity in the afferents are also required to establish normal mappings between the source cells and the target region. Specific mappings arise in these targets because temporal contiguity in firing is somehow transformed into spatial contiguity of synaptic contacts. In this article, we propose a theory that utilizes the covariance of a transient diffusive signal produced at active synapses with the firing of presynaptic axon terminals to account for many of these activity-dependent features of vertebrate neuroanatomy. Computer simulations of the growth of axons within a three-dimensional volume of neural tissue reveal the generality of the proposed mechanism in accounting for the self-organization of a broad range of diverse neuroanatomical structures, including those in the cerebral cortex. The proposed mechanism is consistent with detailed anatomical and physiological data, and direct experimental tests of predictions of the theory are suggested.