Reinterpreting central place networks using ideas from fractals and self-organized criticality

The basic rules of central place networks are abstracted and formulated as three geometric series scaling laws, which can be transformed into several power laws associated with fractal structure. The scaling laws might be the Rosetta Stone to understand the complexity of human geographical systems because they take the form of Horton and Strahler's laws in geomorphology and Gutenberg and Richter's laws in seismology indicative of fractals and self-organized criticality (SOC). An empirical analysis is conducted with the use of data from southern Germany, given by Christaller. The fractal dimensions, D-f, of four systems are calculated as follows: D-f is 1.733 for Munich, 1.685 for Nuremberg, 1.837 for Stuttgart, and 1.481 for Frankfurt. SOC theory is employed to interpret the fractality of central places, and the power laws are seen as signatures of feasible optimality, thus yielding further support to the suggestion that optimality of the system as a whole explains the dynamic origin of fractal forms in nature.