# Christaller's Central Place Theory

### Introduction

Central Place Theory (CPT) is an attempt to explain the spatial arrangement, size, and number of settlements. The theory was originally published in 1933 by a German geographer Walter Christaller who studied the settlement patterns in southern Germany. In the flat landscape of southern Germany Christaller noticed that towns of a certain size were roughly equidistant. By examining and defining the functions of the settlement structure and the size of the hinterland he found it possible to model the pattern of settlement locations using geometric shapes (usually triangles and hexagons). Christaller examined the factors which caused variation or deviation from his and other settlement hierarchy models. It is now possible to incorporate factors which cause the variation in the regular geometry of CPT in the neural network modelling framework. Some of the data necessary to simulate CPT were used in Model 1 including the distance from various sizes of settlements, and the locations and functionality of built up areas.

### Details of the theory

Christaller noted three different arrangements of central places:
1. The marketing principle (K=3 system);
2. The transportation principle (K=4 system);
3. The administrative principle (K=7 system).

Chrystaller found that the number of settlements at any level in either of these hierarchies is directly related to which hierarchy it is.

In a k=3 system for each of the largest settlements in the hierarchy there are on average 3 proximal settlemnents of the next size down in the hierarchy, for each of these again there will be on average 3 proximal settlemnents of the next size down in the hierarchy and so on down the hierarchy to the smallest sized settlement. Christaller noted that this type of hierarchy prevailed where it was most important for society to ensure equal provision of goods and services. Examining the pattern using hexagons Christaller found that central places emerge at the center of a hexagon, containing six lower-order settlements. If transportation costs are to be minimized Chrystaller found that by rotating and enlarging the hexagon that central places emerged where there are 4 proximal settlement of a given size. Finally, for administration purposes Christaller believed the need for 7 proximal settlements of the highest order to drive the creation of the central one into the next order in the hierarchy.

There are various interpretations of Christaller's CPT. Often too much is read into the 3 main systems he studied. The key is the fractal type nature of settlement hierarchies. In the interpretation I've outlined above using proximity K could attain any integer value. It is quite possible that the value of K could be calculated for subareas of Europe and would be helpful in creating EU population surfaces.

Many other geographers and economists have developed theories to explain central places and they have been applied in many areas of the world. The following is a list of links to CPT related web sites: