Scaling laws that describe complex interactions between organisms and their environment as a function of body size offer exciting potential for synthesis in biology(1-4). Home range size, or the area used by individual organisms, is a critical ecological variable that integrates behaviour, physiology and population density and strongly depends on organism size(5-7). Here we present a new model of home range-body size scaling based on fractal resource distributions, in which resource encounter rates are a function of body size. The model predicts no universally constant scaling exponent for home range, but defines a possible range of values set by geometric limits to resource density and distribution. The model unifies apparently conflicting earlier results and explains differences in scaling exponents among herbivorous and carnivorous mammals and birds(5-18). We apply the model to predict that home range increases with habitat fragmentation, and that the home ranges of larger species should be much more sensitive to habitat fragmentation than those of smaller species.