When they reach a flat plain, rivers often deposit their sediment load into a cone-shaped structure called alluvial fan. We present a simplified experimental setup that reproduces, in one dimension, basic features of alluvial fans. A mixture of water and glycerol transports and deposits glass beads between two transparent panels separated by a narrow gap. As the beads, which mimic natural sediments, get deposited in this gap, they form an almost one-dimensional fan. At a moderate sediment discharge, the fan grows quasistatically and maintains its slope just above the threshold for sediment transport. The water discharge determines this critical slope. At leading order, the sediment discharge only controls the velocity at which the fan grows. A more detailed analysis reveals a slight curvature of the fan profile, which relates directly to the rate at which sediments are transported.