Fractal analysis of US settlement patterns

Estimates of fractal mass dimension D are used to characterize the spatial distribution or clustering behavior of human settlements in Pennsylvania, K ansas and Utah. Uniform random and rectangular lattice models are then comp ared to actual settlement patterns using mass dimension as a quantitative m easure of model validity. Data was taken from a United States Geographical Survey geo-coded census database. The distribution of pairwise distances be tween settlements is used to estimate fractal dimension D in the scaling ra nge from 3 to 300 km. Novel analysis methods are shown to reduce small and large scale distortions and increase the range of scaling behaviors for est imating mass dimension. Results show that the settlement patterns have mass dimensions which vary systematically with the visual impression of cluster ing visible in maps of these regions: Kansas D = 1.9, Pennsylvania D = 1.7, Utah D = 1.4, Uniform Random and Rectangular Lattice D = 2., The results d emonstrate the utility of mass dimension when used to compare patterns in a reas of different size and with differing numbers of settlements. Such comp arisons are often impossible using traditional statistical methods. We also demonstrate how neither model captures the clustering behavior of actual s ettlement patterns, and propose that a measure of mass dimension might prov e useful in validating future models of settlement behavior.