Fractal Dimensions Derived from Spatial Allometric Scaling of Urban Form

Abstract

The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric scaling law, which indicates spatial allometry of cities. This paper is devoted to exploring the fractal dimension proceeding from urban spatial allometry. By theoretical reasoning and empirical analysis of urban traffic network, we can derive a set of fractal dimension from the spatial allometry and reveal the basic property of the new fractal parameters. The findings are as follows. First, the fractal dimension values of traffic lines are higher than those of traffic nodes. Second, the fractal dimension values based on variable boundaries are lower than those based on the concentric circles. Conclusions can be reached that the fractal dimensions coming from spatial allometry are a type of correlation dimension rather than capacity dimension, and the relative growth rate of traffic points is greater than that of traffic nodes. This study provides new way of understanding allometry, fractals, and scaling in urban systems.

25 pages, 7 figures, 4 tables

References in corpus (8)

• Power-law distributions in empirical data
• The Matthew effect in empirical data
• Laws of Population Growth
• Languages cool as they expand: Allometric scaling and the decreasing need for new words
• The Distance-Decay Function of Geographical Gravity Model: Power Law or Exponential Law?
• Scaling: Lost in the smog
• Scaling and allometry in the building geometries of Greater London
• Hierarchical Scaling in Systems of Natural Cities

Cited by in corpus (12)

• Fractal Modeling and Fractal Dimension Description of Urban Morphology
• Multifractal scaling analyses of urban street network structure: the cases of twelve megacities in China
• Normalizing and classifying shape indexes of cities by ideas from fractals
• Exploring the Level of Urbanization Based on Zipf's Scaling Exponent
• Defining Urban Boundaries by Characteristic Scales
• Exploring the relationship between the spatial distribution of roads and universal pattern of travel-route efficiency in urban road networks
• Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries
• Characteristic Scales, Scaling, and Geospatial Analysis
• Demonstration of Duality of Fractal Gravity Models by Scaling Symmetry
• Spatial Signal Analysis based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks
• Derivation of Relations between Scaling Exponents and Standard Deviation Ratios
• Geographical Analysis: from Distance-based Space to Dimension-based Space