In the early visual system, cells of the same type perform the same computation in different places of the visual field. How these cells code together a complex visual scene is unclear. A common assumption is that cells of the same type will extract a single stimulus feature to form a feature map, but this has rarely been observed directly. Using large-scale recordings in the rat retina, we show that a homogeneous population of fast OFF ganglion cells simultaneously encodes two radically different features of a visual scene. Cells close to a moving object code linearly for its position, while distant cells remain largely invariant to the object's position and, instead, respond non-linearly to changes in the object's speed. Cells switch between these two computations depending on the stimulus. We developed a quantitative model that accounts for this effect and identified a likely disinhibitory circuit that mediates it. Ganglion cells of a single type thus do not code for one, but two features simultaneously. This richer, flexible neural map might also be present in other sensory systems.