Map transformations of point patterns: Central place patterns in areas of variable population density

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The strategy we have described to determine location patterns of central places on a plain of nonuniform population density is presented as merely one small step in the task of bringing geographic theory closer to reality. At a time when the claim can be made that other facets of the theory are equally well out of touch with reality, some will undoubtedly conclude that these other facets deserve prior attention. They include entrepreneurial behavior and consumer spatial behaviorin fact, the whole marketing system is so naively treated by “classical” theory. Aside from potential applications to central place work, the algorithm is applicable to many current spatial servicing problems. In this respect it may serve as a normative tool in spatial planning. It has further been suggested that only minor modifications are necessary to extend the range of applications from the present emphasis on distributing points to serve equal population-size areas to other cases where distance constraints are imposed for the farthest person to be serviced; or where people are voluntarily choosing service points according to a space-preference function; or where the number of people to be served varies with population density; or where areas encompassing equal travel-time limits or travel-cost limits are desired. In all such cases, the fundamental logic and strategy of manipulating a set of points to best represent a set of local interpoint distances are identical. It is at this level that the isomorphism with multidimensional scaling algorithms which provided the stimulus for this work is to be found.