A new model for vegetation patterns is introduced. The model reproduces a w
ide range of patterns observed in water-limited regions, including drifting
bands, spots, and labyrinths. It predicts transitions from bare soil at lo
w precipitation to homogeneous vegetation at high precipitation, through in
termediate states of spot, stripe, and hole patterns. It also predicts wide
precipitation ranges where different stable states coexist. Using these pr
edictions we propose a novel explanation of desertification phenomena and a
new approach to classifying aridity.