The regular arrangement of leaves around a plant's stem, called phyllotaxis, has for centuries attracted the attention of philosophers, mathematicians and natural scientists; however, to date, studies of phyllotaxis have been largely theoretical. Leaves and flowers are formed from the shoot apical meristem, triggered by the plant hormone auxin. Auxin is transported through plant tissues by specific cellular influx and efflux carrier proteins. Here we show that proteins involved in auxin transport regulate phyllotaxis. Our data indicate that auxin is transported upwards into the meristem through the epidermis and the outermost meristem cell layer. Existing leaf primordia act as sinks, redistributing auxin and creating its heterogeneous distribution in the meristem. Auxin accumulation occurs only at certain minimal distances from existing primordia, defining the position of future primordia. This model for phyllotaxis accounts for its reiterative nature, as well as its regularity and stability.