Energy Flow and Spatial Order Mixed Hexagonal Hierarchies of Central Places

Abstract

r T HE existence and nature of the central-place hierarchy have been hotly debated, and one criticism has been that methods used to detect the hierarchy are subjective and probably biased. In answer to the critics it should be pointed out that a single theory, based on the assumption of a mixed hierarchy of hexagonal market areas, can explain data from places as disparate as southern Germany, Finland, Ghana, Nigeria, Austria, Wales, and Tasmania. Investigators in these countries, using various techniques to define the hierarchy, were unbiased by any knowledge of the model presented here, yet all their investigations seem to support the mixed-hierarchy concept. It will be shown that an equilibrium system results from a mixture of several different central-place hierarchies simultaneously present in these areas. The equilibrium is apparently one of least work and of an approach to the maximum possible entropy, and hence maximum possible probability, for the flow system. Christaller, in his original work,' suggested that central places are arranged in a hexagonal lattice and that each central place is surrounded by a hexagonal market area. This pattern ensures that the entire area is served by central places. Competition between central places is minimized because overlap between circular market areas surrounding neighboring centers is at a minimum when the centers themselves form a hexagonal lattice. Travel distances are economized because the market hexagons are nearly circular. Total demand is at a maximum.2 A hexagonal lattice of markets is also a least-work lattice. In other words, money spent on obtaining an article is divided between transportation cost and the price of the article at the market.