Fractal Systems of Central Places Based on Intermittency of Space-filling

TL;DR

This paper introduces fractal central place models that incorporate intermittency and chance factors, providing a better explanation of real urban settlement patterns through empirical analysis of US cities.

Contribution

It develops a novel fractal-based framework for central place models, integrating intermittency and stochastic elements to align theory with empirical urban patterns.

Findings

Central place networks exhibit self-similarity and fractal properties.

Fractional dimension models better match empirical urban settlement data.

Incorporating chance factors improves the explanation of real-world urban patterns.

Abstract

The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d=2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D<d=2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to well explain the real patterns of urban places. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.