The formation of vegetation patterns in the arid and the semiarid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered pattern in the arid zone. In this "glassy" state, vegetation appears as singular plant spots separated by irregular distances, and an indirect repulsive interaction among shrubs is induced by the competition for water. At higher precipitation rates, the diminishing of hydrological losses in the presence of flora becomes important and yields spatial attraction and clustering of biomass. Turing patterns with characteristic length scale emerge from the disordered structure due to this positive-feedback instability.