Dynamic Central Place Theory: Results of a Simulation Approach

A dynamic central place theory is formulated as a simulation model in which retail activities, described by cost equations, and consumers, described by spatial interaction equations, interact to generate a central place system. The behavior of the model is then examined. Simulation results show that the basic character of the system—whether it is agglomerated or dispersed—depends primarily on a single parameter in the interaction equation, and only secondarily on the specification of the cost function. The results are highly robust in that they are largely independent of the initial sizes and locations of centers, and even independent of the type of interaction equation used. The patterns generated appear plausible.     

Classical Central Places as Protected Thresholds

Previous research efforts demonstrate the use of location covering in the spatial structuring of central places within a single-good context. In a multilevel context, this paper similarly develops a mathematical programming approach to the siting of central places based on the “protection” of inner (or threshold) markets. The objective function maximizes both market coverage of demand and market overlap, subject to an upper bound on market overlap; this allows the formation of different market structures consistent with the various K-valued central place systems of Christaller and Lösch. Siting examples serve to illustrate the working of the protected threshold model in isotropic settings. Furthermore, ways in which the present model might be extended for other situations are examined.     

A Location-Allocation Model of Lösch's Central Place Theory: Testing on a Uniform Lattice Network

This paper develops a location-allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. However, remaining inconsistencies appear to be due to the inability to express the consumer behavior laws as linear constraints, to the bounded and discrete nature of the network, and to the objective function being the sum of integer variables. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions.     

A Dynamic Model of Growth in a Central Place System

A model is developed in which the change in the population distribution of a region is linked to the employment pattern, and this latter in turn to the population distribution through the concepts of central place theory. The result is a dynamic model of interacting urban centers in which the fluctuations (the exact history) of the system play a vital role, and with which the effect of an infrastructure decision can be estimated in the long term.     

The Fractal Theory of Central Place Geometry: A Diophantine Analysis of Fractal Generators for Arbitrary Löschian Numbers

We develop material to determine whether or not an arbitrary number is Löschian; the procedure embodied in the theorems achieves the desired result more swiftly than do previous solutions to this problem. The correspondence between a partition of the central place lattice and a quadratic form permits the rapid determination of the lattice coordinates of an arbitrary Löschian number and of the exact shape of a single fractal generator used to form an entire central place hierarchy associated with an arbitrary Löschian number. Central place hierarchies may be generated geometrically using a single shape applied initially to a hexagon and subsequently, scaled appropriately, to resultant polygons. Fractional dimensions of arbitrary central place hierarchies, measuring their “space-filling” characteristics, follow naturally from this general procedure.     

Empirical Urban Theory for Archaeologists

I review several bodies of empirical urban theory relevant to the archaeological analysis of ancient cities. Empirical theory is a type of “middle-range theory” (following Robert Merton): sets of concepts and methods that are less abstract, and have greater empirical content, than high-level social theory. The categories of theory reviewed here include environment-behavior theory, architectural communication theory, space syntax, urban morphology, reception theory, generative planning theory, normative theory, and city size theory. Most of these approaches originated in the fields of architecture, planning, and geography, and they directly link the urban-built environment to the actions of people within cities.     

Unpacking Central Place Geometry I: Single Level Theoretical k Systems

This paper examines the spatial and potential economic consequences of relaxing the geometrical packing requirement of classical central place theory. Diagrams are used to demonstrate that geometric packing is not necessary to satisfy demand at all discrete points at a given hierarchical level. With unpacked landscapes the same population can be served from fewer, more widely spaced, central places without increasing the length of journey to shop. Consumers have fewer choices in an unpacked landscape, but economies of scale may increase the array of consumer goods and services available. Relaxing the packing requirement allows the development of a range of stable k systems (i.e., further market entry is disallowed). Between the limits of the k = 3 system (Christaller's marketing principle) and the k = 7 system (the sociopolitical or administrative principle), a range of unpacked k systems can develop including a k = 5 and a k = 6 system. Noninteger k systems are also possible as are systems which are stable mixtures of coexisting k principles. In certain instances, it is economically advantageous for two or more entrepreneurs to co-locate in the same central place rather than attempting monopolistic control over a more limited hinterland. Such a result is consistent with both Berry and Garrison's concept of the duplication ratio and with recent trends in retail location.     

A Hierarchical Migration Model of Population Redistribution within a Central Place Hierarchy

A simple hierarchical migration model is proposed as a mechanism for the redistribution of population within a Christaller central place hierarchy. Given a predefined functional hierarchy, the migration process causes any initial population distribution to converge to an equilibrium distribution. Under certain special conditions, the equilibrium is identical to a central place population distribution derived from economic base concepts.     

An Empirical Evaluation of Profit Cycle Theory

This study tests key hypotheses of Markusen's profit cycle theory of regional growth by examining the recent time path of industrial development for eight U.S. sectors. The analysis uses annual data for 1954–1990 and incorporates the influence of national economic trends and random effects in identifying stages of the profit cycle. Based upon those stages, the hypothesized changes in the behavior of other aspects of the growth cycle are assessed in simple statistical models. The results of the empirical tests are mixed. Employment follows a general pattern of early rapid growth followed by slow growth and eventually decline, but the pattern is not symmetric. The value-added curves are similarly asymmetric, and some even contradict the expected monotonicity of the growth and decline process. The lack of spatial dispersion is probably the most striking result of the study. The stability over time of the employment percentage in top states is inconsistent with the spatial dispersion implications of the profit cycle model.     

A Theory of Reduplication: Eightfold Meters in Classical Persian Poetry

It is a known fact that classical Persian poets were partial to poetic meters composed of eight feet, known as muthamman. On this topic, however, two issues remain unsolved: How did the Persian poets devise these meters in the first place? Despite their flagrant predilection for eightfold meters, why did the Persians never use such meters as sarī? and qarīb in this form? This paper argues that the Persians, influenced by the structure of the Arabic eightfold base meters, crafted their muthamman meters after a specific process of reduplication. This theory also accounts for the lack of eightfold sarī? and qarīb meters, their structure being incompatible with the reduplication process.