The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered patterns in the arid zone. In this "glassy" state, vegetation appears as a 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 diminish of hydrological losses in the presence of flora becomes important and yields spatial attraction and clustering of biomass. Turing-like patterns with characteristic length scale may emerge from the disordered structure due to this positive feedback instability.PACS numbers: 87.23. Cc, 89.75.Kd, 45.70.Qj Vegetation patterns in the arid and the semi-arid climatic zones [1,2] are an interesting example of spontaneous symmetry breaking in complex systems. Competition of shrubs for a limited supply of water is the relevant process that dictates the spatial organization. The struggle for water induces an indirect interaction among shrubs, as the flora extinct if its water supply is insufficient.Competition for common resource has been considered for many years as one of the basic processes in population dynamics [3,4]. It may be shown that, if two species compete for a common resource, the one that is able to survive at a lower resource level prevails and displaces the other species population. Stable coexistence of N species is possible if there exist N different resources and each of the species is a superior competitor for one of the supplies, that is, it has one biological niche.The situation becomes more complicated if the resource admits spatial dynamics. Recent theoretical and experimental work reveals the dynamics of competing populations in water, where light, the limiting resource, is consumed gradually by the upper layers of aquatic phytoplankton [5]. This model may be extended to include spatial dynamics of the fauna, but it does not support time independent patterning . Vegetation patterns are an example of one species (shrubs) and one resource (water) system, where field studies revealed wide variety of stable, or almost stable, spontaneous segregation modes. Understanding the underlying mechanism for generation of such patterns and their observed resilience is considered as an important step toward a comprehension of the desertification process, where environmental effects like climate changing and grazing destroys the natural balance toward stable aridity.Technically, the water-biomass system has been considered as a spatially extended nonlinear system, that, in some parameter range, may yield stripes, spots, labyrinth and other ordered arrangements attributed to a positive feedback mechanism, i.e., to the inhibition of water runoff and evaporation by the flora [6]. However, the typical perennial vegetation patterns in the semi-arid zone are disordered, as one can easily see in Fig. (1). The generic spatial organization of perennial fl...
