The branched fractal structures formed by non-equilibrium electrodeposition of metals’ have for several years been considered as model systems for the study of branching and fractal growth processes generally(2-6). Most studies have focused on the large-scale structure of the deposits, but the question of how the branching pattern emerges from the nucleation and growth of the polycrystalline metal at the microscopic scale remains unclear. Here I present experimental and theoretical results which suggest that branched electrodeposits may arise from an oscillatory character in the nucleation kinetics. For this kind of deposition, nucleation is probabilistic but biased towards higher electric fields. I suggest that a given nucleation event is followed by a recovery phase before a subsequent event is possible. This oscillatory nature generates a polycrystalline deposit, the grain size of which determines the level of ’noise’ which is amplified by the familiar laplacian (’fingering’) instabilities of non-equilibrium growth(2-6) into a macroscopically fractal structure.