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.     

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.     

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.     

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.     

A Comparison of Simple Lattice Transport Networks for a Uniform Plain

The objective is to compare construction and transport costs for triangular, orthogonal, and hexagonal regular lattices as transport networks serving a uniform, unbounded plain. The lattices are standardized so that the average distance from the elementary area to the edge is the same for each. This standardization results in equal construction costs for the three networks; thus, the comparison can be made in terms of route factors, which favors the triangular lattice over the other two.     

The Lösch System of Market Areas: Derivation and Extension

Certain aspects of Lösch's classic work on the network of markets and the system of networks have not yet been clearly explained in the literature. Lösch did not describe his derivation procedures in full, and apparent printing errors in certain förmulae confuse the issue further, with the result that several recent texts reproduce Lösch's diagrams but offer no explanation of how they are constructed. Accepting the network of hexagonal market areas for a continuous system of markets, given an even but discrete distribution of population, the derivation from first principles of the complete system of different market areas is presented. Apparent errors in the translated text of Lösch's work are corrected. Limitations in some other authors' work and accordance with earlier empirically derived formulae are mentioned. The production of “city-rich” and “city-poor” sectors is shown to be a constraint on, rather than a result of, the system, and Lösch's statement that the coincidence of centers is maximized is clarified. The extension of the Lösch system to the internal tertiary structure of the city is presented and attention drawn to the empirical attractiveness of this approach.     

The Future of Collective Farms' Built Social Infrastructure: Choosing Between Central Place and Network Theories

The aim of this paper is to discuss local and regional planning and development practices in a post‐socialist country such as Estonia. Two approaches — central places and network theories — are used as a conceptual basis. According to the first hypothesis, planning and development of social infrastructure (e.g. schools, sports halls) has remained based on the central place theory — as an outdated planning approach — in Estonia. The second hypothesis argues that while, on the one hand, the application of the network paradigm and increased cooperation between local communities would considerably save public resources, on the other hand, because of the path dependency of Soviet centralized planning and development practices, the networking and lobbying takes place vertically rather than horizontally. This restricts both administrative cooperation and networking on the local and regional levels. The paper consists of three parts. The first part describes the turn in Western planning theory: the shift from normative top‐down planning to a bottom‐up approach and networking. The second part analyses critically the Soviet and post‐Soviet planning theory and practices: the planning and development culture created during the Soviet era. Finally we present a case study of a community planning procedure in the Suure‐Jaani locality — a good example of the influence of historical changes in the settlement system and planning culture of the past on current development.     

The Price Theory of Thünen's Theory of Rent: Assumptions and Implications of a Familiar Model

Economic forces in the Thünen rent diagram and the equivalence of certain Thünian and Ricardian land rent concepts are shown diagrammatically. The usual, linear rent line requires fixed production coefficients in agriculture and constant costs in transportation. The ability to substitute among land and other inputs in agriculture makes the rent line convex to the origin, as do decreasing costs in transportation. Increasing cost transportation makes the rent line concave. Traditional, subsistence agriculture is likely to produce a more strongly convex rent line than modern, large-scale agriculture.
Les forces économiques dans le diagramme de rente de Thünen et l'equivalence de certains concepts de rente foncier Thünien et Ricardien sont exposés graphiquement. La courbe de rente linéaire exige des coëfficients de production fixes en agriculture et des coûts de transport fixes. La capacitéà substituer entre la terre et d'autres facteurs de production en agriculture, ainsi que des coûts de transport décroissants, donnent une courbe de rente convexe par rapport à 1'origine. Des coûts de transport accroissants donnent une courbe de rente concave. Une agriculture à petite échelle, traditionnelle, donnera probablement une courbe de rente plus convexe qu'une agriculture moderne, à grande échelle.     

"A Troubled Godless Place": Catholic Practice and Local Politics in the Communes of the Central Vaucluse, 1830–1905

In the final quarter of the nineteenth century, men and women in the French communes of the central Vaucluse began to defer or neglect vital Catholic rites of passage. Against a backdrop of turbulent regional politics and economic upheaval, formal adherence to church doctrine declined sharply, never again to regain its previous levels. This article assesses the religious gestures of individuals and communities through the analysis of their sacramental participation, the only recorded response of Catholics to the church's presence in their lives. The implementation of the lay republic in the community by means of both local and national secularizing policy from 1878 to 1905 was the primary precipitant of general, dramatic decreases in formal Catholic practice. It was only upon the official secularization of communal society and politics that significant numbers of central Vauclusiens began to relinquish their attachment to Catholic rites of passage surrounding birth, marriage, and death.     

SANET: A Toolbox for Spatial Analysis on a Network

This article shows a geographical information systems (GIS)-based toolbox for analyzing spatial phenomena that occur on a network (e.g., traffic accidents) or almost along a network (e.g., fast-food stores in a downtown). The toolbox contains 13 tools: random point generation on a network, the Voronoi diagram, the K -function and cross K -function methods, the unconditional and conditional nearest-neighbor distance methods, the Hull model, and preprocessing tools. The article also shows a few actual analyses carried out with these tools.