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Fractal Analysis Based on Hierarchical Scaling in Complex Systems
Yanguang Chen
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indica…
Spatial Analysis of Cities Using Renyi Entropy and Fractal Parameters
Yanguang Chen, Jian Feng
The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex dis…
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Yanguang Chen
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension sugges…
A New Model of Urban Population Density Indicating Latent Fractal Structure
Yanguang Chen
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the research…
Normalizing and classifying shape indexes of cities by ideas from fractals
Yanguang Chen
A standard scientific study comprises two processes: one is to describe a thing, and the other is to understand how the thing works. In order to understand the principle of urban g…
Hierarchical Scaling in Systems of Natural Cities
Yanguang Chen, Bin Jiang
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is alw…
Equivalent Relation between Normalized Spatial Entropy and Fractal Dimension
Yanguang Chen
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi…
Modeling Growth Curve of Fractal Dimension of Urban Form of Beijing
Yanguang Chen, Linshan Huang
The growth curves of fractal dimension of urban form take on squashing effect and can be described by sigmoid functions. The fractal dimension growth of urban form in western count…
Understanding Fractal Dimension of Urban Form through Spatial Entropy
Yanguang Chen, Jiejing Wang, Jian Feng
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 t…
A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014
Yanguang Chen, Jian Feng
The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily in…
Fractal-Based Exponential Distribution of Urban Density and Self-Affine Fractal Forms of Cities
Yanguang Chen, Jian Feng
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to…
Modeling Fractal Structure of Systems of Cities Using Spatial Correlation Function
Yanguang Chen, Shiguo Jiang
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed rando…
New Approaches for Calculating Moran's Index of Spatial Autocorrelation
Yanguang Chen
Spatial autocorrelation plays an important role in geographical analysis, however, there is still room for improvement of this method. The formula for Moran's index is complicated,…
Logistic Models of Fractal Dimension Growth for Spatio-Temporal Dynamics of Urban Morphology
Yanguang Chen
Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the…
A comparison between two OLS-based approaches to estimating urban multifractal parameters
Linshan Huang, Yanguang Chen
Multifractal theory provides a new spatial analytical tool to describe urban form and growth, but many basic problems remain to be solved. Among various pending issues, the most si…