A model for a simple and possibly very common mechanism to produce patchiness is presented. It is shown that patchiness is an inevitable consequence simply of dispersal in a randomly fluctuating environment. The measurement of patchiness using the variance spectrum is discussed. A linearized model for population dynamics in a spatially and temporally varying environment is introduced and analyzed. Explicit formulae are obtained for the equilibrium spatial pattern of the population as a function of the spatial pattern of the resource abundance and of the population''s rate of increase and dispersal characteristics.