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In the developing mammalian retina, spontaneous waves of action potentials are present in the ganglion cell layer weeks before vision. These waves are known to be generated by a synaptically connected network of amacrine cells and retinal ganglion cells, and exhibit complex spatiotemporal patterns, characterized by shifting domains of coactivation. Here, we present a novel dynamical model consisting of two coupled populations of cells that quantitatively reproduces the experimentally observed domain sizes, interwave intervals, and wavefront velocity profiles. Model and experiment together show that the highly correlated activity generated by retinal waves can be explained by a combination of random spontaneous activation of cells and the past history of local retinal activity.