A model of self-organization of synapses in the striate cortex is described, and its functional implications discussed. Principal assumptions are: (a) covariance of cell firing declines with distance in cortex, (b) covariance of stimulus characteristics declines with distance in the visual field, and (c) metabolic rates are approximately uniform in all small axonal segments. Under these constraints, Hebbian learning implies a maximally stable synaptic configuration corresponding to anatomically and physiologically realistic ‘‘local maps’’, each of macro-columnar size, and each organized as Möbius projections of a “global map” of retinotopic form. Convergence to the maximally stable configuration is facilitated by the spatio-temporal learning rule. A tiling of V1, constructed of approximately mirror-image reflections of each local map by its neighbors, is formed. The model supplements standard concepts of feed-forward visual processing by introducing a new basis for contextual modulation and neural network identifications of visual signals, as perturbation of the synaptic configuration by rapid stimulus transients. On a long time-scale, synaptic development could overwrite the Möbius configuration, while LTP and LTD could mediate synaptic gain on intermediate time-scales.