THE similarity of many patterns formed in non-equilibrium growth processes in physics, chemistry and biology is conspicuous, and many attempts have been made to discover common mechanisms underlying their formation(1). A central question is what causes some patterns to be dendritic (symmetrically branched, like snowflakes) and others fractal (randomly ramified). In general, the transition from fractal to dendritic growth is regarded as a manifestation of the predominance of anisotropy over random noise in the growth process. In electrochemical deposition, this transition is observed as the growth speed is varied(2,3). Here we report a crossover from fractal to dendritic growth in two dimensions on the microscopic scale. We use the scanning tunnelling microscope to study diffusion-limited aggregation of silver atoms on a Pt(111) surface. The transition occurs as the deposition flux is increased, and our observations suggest that the increasing importance of anisotropy of edge diffusion at higher flux is responsible for this crossover. We anticipate that a similar phenomenon may operate in three-dimensional crystal growth.