FRACTAL ANALYSIS OF US SETTLEMENT PATTERNS

Abstract

Estimates of fractal mass dimension D are used to characterize the spatial distribution or clustering behavior of human settlements in Pennsylvania, Kansas and Utah. Uniform random and rectangular lattice models are then compared to actual settlement patterns using mass dimension as a quantitative measure of model validity. Data was taken from a United States Geographical Survey geo-coded census database. The distribution of pairwise distances between settlements is used to estimate fractal dimension D in the scaling range 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 estimating mass dimension. Results show that the settlement patterns have mass dimensions which vary systematically with the visual impression of clustering 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 demonstrate the utility of mass dimension when used to compare patterns in areas of different size and with differing numbers of settlements. Such comparisons are often impossible using traditional statistical methods. We also demonstrate how neither model captures the clustering behavior of actual settlement patterns, and propose that a measure of mass dimension might prove useful in validating future models of settlement behavior.