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In this paper, we address the question whether and through which mechanisms herbivores can induce spatial patterning in savanna vegetation, and how the role of herbivory as a determinant of vegetation patterning changes with herbivore density and the pre‐existing pattern of vegetation. We thereto developed a spatially explicit simulation model, including growth of grasses and trees, vertical zonation of browseable biomass, and spatially explicit foraging by grazers and browsers. We show that herbivores can induce vegetation patterning when two key assumptions are fulfilled. First, herbivores have to increase the attractiveness of a site while foraging so that they will revisit this site, e.g. through an increased availability or quality of forage. Second, foraging should be spatially explicit, e.g. when foraging at a site influences vegetation at larger spatial scales or when vegetation at larger spatial scales influences the …