Ephrin-As act as retinal topographic mapping labels, but the molecular basis for two key aspects of mapping remains unclear. First, although mapping is believed to require balanced opposing forces, ephrin-As have been reported to be retinal axon repellents, and the counterbalanced force has not been molecularly identified. Second, although graded responsiveness across the retina is required for smooth mapping, a sharp discontinuity has instead been reported. Here, an axon growth assay was developed to systematically vary both retinal position and ephrin concentration and test responses quantitatively. Responses varied continuously with retinal position, fulfilling the requirement for smooth mapping. Ephrin-A2 inhibited growth at high concentrations but promoted growth at lower concentrations. Moreover, the concentration producing a transition from promotion to inhibition varied topographically with retinal position. These results lead directly to a mapping model where position within a concentration gradient may be specified at the neutral point between growth promotion and inhibition.