Central Place Theory (CPT) is an attempt to explain the spatial arrangement, size, and number of settlements. Central place theory is an economic theory which explains patterns of urbanization and establishment of market areas for different goods and services. 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 modeling framework. .
Christaller noted three different arrangements of central places: the marketing principle K=3 system, the transportation principle K=4 system, 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 settlements of the next size down in the hierarchy. For each of these again there will be on average 3 proximal settlements 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.