MAP TRANSFORMATIONS OF POINT PATTERNS: CENTRAL PLACE PATTERNS IN AREAS OF VARIABLE POPULATION DENSITY

A system of central places can be construed as a pattern of points from each of which a group of entrepreneurs serves a surrounding hinterland. These a r e expected to be uniform in population size for any class of center. Where environmental conditions a re uniform, the point patterns of producers are typically uniform. However, where relevant environmental conditions are spatially variable, corresponding point patterns become distorted. In the case of central place patterns, empirical proof that such distortions occur were provided by King [12] who showed that patterns of central places were most uniform in those areas of the United States where manufacturing activities were largely absent and where population densities were most uniform. More sensitive tests by King [13] confirmed the earlier study by showing that, among randomly selected towns in the United States, the distance separating a town from its nearest neighbor of the same size or larger was inversely related to local population density. Though these results are consistent with central place theory [2], no satisfactory reformulation of the theory has been made to take account of the nonuniform environment in a formal sense. Considering the widespread occurrence of these conditions, a reformulated theory from which could be derived a point pattern satisfying the traditional criteria used in central place models would be most useful. Such a model is proposed here, but first some earlier research on this question is reviewed.