Understanding Fractal Dimension of Urban Form through Spatial Entropy
Yanguang Chen, Jiejing Wang, Jian Feng
TL;DR
This paper explores the relationship between spatial entropy and fractal dimension in urban form analysis, demonstrating that fractal dimension provides a scale-invariant characteristic that correlates with entropy measures.
Contribution
It introduces a novel analogy between urban patterns and fractals, clarifies the connection between entropy and fractal dimension, and empirically validates their relationship in city analysis.
Findings
Fractal dimension remains stable across scales, unlike spatial entropy.
A clear correlation exists between entropy and fractal dimension at small scales.
Fractal dimension can serve as a characteristic measure for urban form analysis.
Abstract
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal parameters can be employed to characterize scale-free phenomena. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on different entropy concepts. Three representative fractal dimensions in the multifractal dimension set are utilized to make empirical analyses of urban form of two cities. The results show that the entropy values are not determinate, but the fractal dimension value is certain; if the linear size of boxes is small enough (e.g., <1/25), the…
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