Recursive Subdivision of Urban Space and Zipf's law
arXiv:1209.5544 · doi:10.1016/j.physa.2013.10.022
Abstract
Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law and can be characterized with the rank-size rule. A model of spatial disaggregation of urban space is presented to depict the spatial regularity of urban growth. By recursive subdivision of space, an urban region can be geometrically divided into two parts, four parts, eight parts, and so on, and form a hierarchy with cascade structure. If we rank these parts by size, the portions will conform to the Zipf distribution. By means of GIS technique and remote sensing data, the model of recursive subdivision of urban space is applied to three cities of China. The results show that the intra-urban hierarchy complies with Zipf's law, and the values of the rank-size scaling exponent are very close to 1. The significance of this study lies in three aspects. First, it shows that the strict subdivision of space is an efficient approach to revealing spatial order of urban form. Second, it discloses the relationships between urban space-filling process and the rank-size rule. Third, it suggests a new way of understanding fractals, Zipf's law, and spatial organization of urban evolution.
23 pages, 7 figures, 6 tables
References in corpus (11)
- Laws of Population Growth
- Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words
- Street Hierarchies: A Minority of Streets Account for a Majority of Traffic Flow
- Bankruptcy risk model and empirical tests
- The Rank-Size Scaling Law and Entropy-Maximizing Principle
- The Mathematical Relationship between Zipf's Law and the Hierarchical Scaling Law
- Modeling fractal structure of city-size distributions using correlation function
- Measuring Urban Sprawl Based on Massive Street Nodes and the Novel Concept of Natural Cities
- Zipf's law, 1/f noise, and fractal hierarchy
- Zipf's law, Hierarchical Structure, and Shuffling-Cards Model for Urban Development
- Scale invariant properties of public debt growth