Summary: Spatially periodic vegetation patterns are observed in many semiarid regions. They are classified according to their symmetry as vegetation stripes on hillsides or spotted patterns on flat ground. We propose a simple model based on the interactions among water, soil and vegetation, which gives a systematic description of the variety of vegetation patterns. First, it describes most characteristics of vegetation stripes investigated in field observations and agrees with the hypothesized origin of vegetation stripes deduced from field observations, the spatially heterogeneous infiltration rate of surface water into soil. Moreover, it indicates that spotted patterns emerge from the same dynamics. Second, the pattern selection derived from the model is consistent with that found in real phenomena, i.e., predominantly bare ground with spotted vegetation in the most severe environments, banded patterns in intermediate environments and nearly continuous vegetation with spotted bare ground in the most favorable environments.