Hypotheses about the origin of vegetation pattern formation in semi-arid areas around the world almost all include a common feature of semi-arid areas: the presence of a positive feedback between plant density and water infiltration. We investigate whether this positive feedback and the spatial redistribution of runoff water are sufficient to explain vegetation pattern formation. For this purpose, we analyze a spatially explicit model consisting of partial differential equations using a method for demonstrating pattern formation (Turing analysis). Our analysis reveals that pattern formation can occur in semi-arid areas given only the positive feedback between plant density and local water infiltration coupled with the spatial redistribution of runoff water. Thus, slope and underlying heterogeneity are not essential conditions. Keywords: grazing, herbivory, patchiness, plant dispersal, plant-soil interaction, positive feedback, runoff, semi-arid grazing systems, spatially explicit model, Turing analysis, vegetation patterns.