Geographism: Central Place Theory and Voronoi Diagram.

I think it is time to post some core theories- Central place theory (CPT) and Voronoi diagram. So be ready to give your brain quite an exercise!

Originally developed by Walter Christaller in 1933, Central place theory is the idea that urban locations are arranged spatially in a pattern of hexagons that are nested based on the size of the urban location. Rather explaining whole theory, I like to put in front of you a short video summarizing the concept.

This concept has been called Unrealistic. However, it is able to imitate existing urban system (i.e by applying K=3, K=4, and K=7 method). CPT attempts to illustrate how settlements locate in relation to one another, the amount of market area a central place can control, and why some central places function as hamlets, villages, towns, or cities.

It is also one of the most widely studied models of retail location and market area patterns.

While the CPT is a concept on spatial- temporal relationship, the Voronoi Adjacency graph could be valuable tools for the manipulation of spatial adjacency relationship in a computer environment for a variety of application.

One of the articles I had studied few years back illustrated retail location and market area pattern by using higher-order Voronoi diagrams. These diagrams construct market areas based on the assumption that consumers choose from a set of k (where k = 1 to n number) nearest centers of the same hierarchical level. The appropriate market areas are given by the order-k Voronoi design. If I am remembering it right, it is the article named ‘Relaxing the nearest centre assumption in central place theory’.

Here is the Voronoi-Style US Maps with a current location of state capitals and simulated new boundaries constructed so that every place within the polygon is nearest to its capital city. (special thanks to my friend Kristi who cared to find these great maps in the first place. Here is Kristi's Posts - "Voronoi Diagramming and GIS" and "Voronoi II")