Multifractal Characterization of the Distribution Pattern of the Human Population

The generalized entropy, calculated from the quadrat counts of the population of the United States and Great Britain, is plotted against the logarithm of the quadrat size. These graphs are linear over a range of scales that corresponds to the size of a city up to the size of the country. This linearity indicates a strong scale-invariant component to the spatial population distribution pattern. Measurements of the generalized q-dimensions and alpha spectrum of the spatial population distribution patterns estimated from these graphs are presented.