Fractal Texture and Structure of Central Place Systems

TL;DR

This paper develops a theoretical framework to derive structural fractals of central place systems from their textural fractals, linking fractal dimensions to real-world settlement patterns and urban evolution.

Contribution

It introduces a method to convert textural fractal dimensions into structural fractal dimensions, enabling analysis of human settlement systems using fractal geometry.

Findings

Classic models include Koch snowflake and Sierpinski curves.

Traffic principles influence urban and rural evolution.

Textural fractal dimensions can be converted into structural dimensions.

Abstract

The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines, but it cannot be directly applied to spatial structure of real human settlement systems. To solve this problem, this paper is devoted to deriving structural fractals of central place models from the textural fractals. The method is theoretical deduction based on the dimension rules of fractal sets. The textural fractals of central place models are reconstructed, the structural dimensions are derived from the textural dimensions, and the central place fractals are formulated by the k numbers and g numbers. Three structural fractal models are constructed for central place systems according to the corresponding fractal dimensions. A theoretical finding is that the classic central place models comprise Koch snowflake curve and Sierpinski space filling curve, and an inference is that the traffic principle plays a leading role in urban and rural evolution. The conclusion can be reached that the textural fractal dimensions can be converted into the structural fractal dimensions. The latter dimensions can be directly used to appraise urban and rural settlement distributions in the real world. Thus, the textural fractals can be indirectly utilized to explain the development of the systems of human settlements.