The occurrence of patches of vegetation alternating with patches of (almost) bare soil (''vegetation pattern formation'') is a common feature in arid and semi-arid grazing systems throughout the world. These systems cover nearly 30% of the earth's land surface. Vegetation patches vary in form, ranging from irregular mosaics to regular bands, and patch sizes range from approximately one to hundreds of meters. Vegetation pattern formation may occur on flat ground as well as on gentle slopes. An illustrative example of vegetation pattern formation is the so called 'tiger bush' on gentle slopes in sub-Saharan Africa. In this particular case, vegetation patches consisting of grasses, shrubs, trees, or any combination of these functional groups, appear as regular bands alternating with bare soil resembling stripes of a tiger skin when seen from the air.