scholarly journals Modeling Urban Growth and Form with Spatial Entropy

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yanguang Chen
Keyword(s):  
Fractal Dimension ◽  
Urban Growth ◽  
Urban Form ◽  
Growth Models ◽  
Logistic Function ◽  
Measurement Scale ◽  
Spatial Complexity ◽  
Entropy Increase ◽  
Fractal Models ◽  
Spatial Entropy

Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using the fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In the absence of the scaling property, we can make use of the entropy function and measurements. This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived, and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Furthermore, multifractal dimension spectra are generalized to spatial entropy spectra. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities.

scholarly journals Fractal-Based Modeling and Spatial Analysis of Urban Form and Growth: A Case Study of Shenzhen in China

2020 ◽  
Vol 9 (11) ◽  
pp. 672
Author(s):  
Xiaoming Man ◽  
Yanguang Chen
Keyword(s):  
Fractal Dimension ◽  
Urban Growth ◽  
Urban Form ◽  
Fractal Structure ◽  
Southern China ◽  
Growth Curves ◽  
Northern China ◽  
Logistic Function ◽  
Urban Region ◽  
The Common

Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension curves of urban growth in Western countries follow the common logistic function, while the fractal dimension growth curves of cities in northern China follow the quadratic logistic function. Now, we want to investigate whether other Chinese cities, especially cities in South China, follow the same rules of urban evolution and attempt to analyze the reasons. This paper is devoted to exploring the fractals and fractal dimension properties of the city of Shenzhen in southern China. The urban region is divided into four subareas using ArcGIS technology, the box-counting method is adopted to extract spatial datasets, and the least squares regression method is employed to estimate fractal parameters. The results show that (1) the urban form of Shenzhen city has a clear fractal structure, but fractal dimension values of different subareas are different; (2) the fractal dimension growth curves of all the four study areas can only be modeled by the common logistic function, and the goodness of fit increases over time; (3) the peak of urban growth in Shenzhen had passed before 1986 and the fractal dimension growth is approaching its maximum capacity. It can be concluded that the urban form of Shenzhen bears characteristics of multifractals and the fractal structure has been becoming better, gradually, through self-organization, but its land resources are reaching the limits of growth. The fractal dimension curves of Shenzhen’s urban growth are similar to those of European and American cities but differ from those of cities in northern China. This suggests that there are subtle different dynamic mechanisms of city development between northern and southern China.

scholarly journals Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Yanguang Chen
Keyword(s):  
Fractal Dimension ◽  
Urban Growth ◽  
Urban Form ◽  
Wave Spectrum ◽  
Fractal Dimensions ◽  
Wave Number ◽  
Similar Distribution ◽  
Image Dimension ◽  
Radial Dimension ◽  
The Fourier Transform

The Fourier transform and spectral analysis are employed to estimate the fractal dimension and explore the fractal parameter relations of urban growth and form using mathematical experiments and empirical analyses. Based on the models of urban density, two kinds of fractal dimensions of urban form can be evaluated with the scaling relations between the wave number and the spectral density. One is theradial dimensionof self-similar distribution indicating the macro-urban patterns, and the other, the profile dimension of self-affine tracks indicating the micro-urban evolution. If a city's growth follows the power law, the summation of the two dimension values may be a constant under certain condition. The estimated results of the radial dimension suggest a new fractal dimension, which can be termed “image dimension”. A dual-structure model namedparticle-ripple model(PRM) is proposed to explain the connections and differences between the macro and micro levels of urban form.

scholarly journals LOGISTIC MODELS OF FRACTAL DIMENSION GROWTH OF URBAN MORPHOLOGY

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850033 ◽  
Author(s):  
YAN-GUANG CHEN
Keyword(s):  
Fractal Dimension ◽  
Urban Form ◽  
Missing Values ◽  
Logistic Models ◽  
Developed Countries ◽  
Logistic Function ◽  
Urban Morphology ◽  
City Development ◽  
Spatial Form ◽  
The Developed Countries

Urban form can be described with fractal dimension, which is a measurement of space filling of urban evolution. However, how to model and understand the fractal dimension growth of urban morphology are still pending questions. This paper is devoted to the research on the fractal dimension curves of urban growth. The principle of squashing function and empirical evidences are employed to demonstrate the following inference: the fractal dimension time series of a city’s spatial form take on a sigmoid curve. Among various sigmoid functions, the logistic function is the most probable selection. The observational data of fractal dimension of different cities from different sources support this logic judgment. A further discovery is that the fractal dimension curves of cities in the developed countries differ from those in the developing countries. A generalized logistic function is thus proposed to model the fractal dimension curves of different types of cities. The general logistic models can be used to predict the missing values and estimate the growth rates of fractal dimension of city development. Moreover, these models can be utilized to analyze when and where there is a fractal of urban form.

scholarly journals Analyzing the Spatiotemporal Uncertainty in Urbanization Predictions

2021 ◽  
Vol 13 (3) ◽  
pp. 512
Author(s):  
Jairo Alejandro Gómez ◽  
ChengHe Guan ◽  
Pratyush Tripathy ◽  
Juan Carlos Duque ◽  
Santiago Passos ◽  
...  
Keyword(s):  
Urban Growth ◽  
Geographical Information Systems ◽  
Growth Models ◽  
A Priori ◽  
Remote Sensing Data ◽  
Public Utility ◽  
Town Planning ◽  
Geographical Information ◽  
New Town ◽  
Spatiotemporal Uncertainty

With the availability of computational resources, geographical information systems, and remote sensing data, urban growth modeling has become a viable tool for predicting urbanization of cities and towns, regions, and nations around the world. This information allows policy makers, urban planners, environmental and civil organizations to make investments, design infrastructure, extend public utility networks, plan housing solutions, and mitigate adverse environmental impacts. Despite its importance, urban growth models often discard the spatiotemporal uncertainties in their prediction estimates. In this paper, we analyzed the uncertainty in the urban land predictions by comparing the outcomes of two different growth models, one based on a widely applied cellular automata model known as the SLEUTH CA and the other one based on a previously published machine learning framework. We selected these two models because they are complementary, the first is based on human knowledge and pre-defined and understandable policies while the second is more data-driven and might be less influenced by any a priori knowledge or bias. To test our methodology, we chose the cities of Jiaxing and Lishui in China because they are representative of new town planning policies and have different characteristics in terms of land extension, geographical conditions, growth rates, and economic drivers. We focused on the spatiotemporal uncertainty, understood as the inherent doubt in the predictions of where and when will a piece of land become urban, using the concepts of certainty area in space and certainty area in time. The proposed analyses in this paper aim to contribute to better urban planning exercises, and they can be extended to other cities worldwide.

scholarly journals A spatial zoning approach to calibrate and validate urban growth models

2016 ◽  
Vol 31 (4) ◽  
pp. 763-782 ◽  
Author(s):  
Ali Kazemzadeh-Zow ◽  
Saeed Zanganeh Shahraki ◽  
Luca Salvati ◽  
Najmeh Neisani Samani
Keyword(s):  
Urban Growth ◽  
Growth Models

scholarly journals Influence of Urban-Growth Pattern on Air Quality in China: A Study of 338 Cities

2018 ◽  
Vol 15 (9) ◽  
pp. 1805 ◽  
Author(s):  
Yanchuan Mou ◽  
Yan Song ◽  
Qing Xu ◽  
Qingsong He ◽  
Ang Hu
Keyword(s):  
Air Pollution ◽  
Air Quality ◽  
Urban Growth ◽  
Growth Pattern ◽  
Urban Form ◽  
Northwest China ◽  
City Size ◽  
Socioeconomic Indicators ◽  
Economic Zones ◽  
Coastal China

Air pollution in China is a serious problem and an inevitable threat to human health. This study evaluated the relationship between air quality and urban growth pattern in China by conducting empirical research involving 338 prefecture-level and above cities. Spatial regression techniques considering spatial autocorrelation were applied to correct the calculation bias. To obtain local and accurate results, a conception of eight economic zones was adopted to delineate cities into different groups and to estimate regression separately. An additional six urban form and socioeconomic indicators served as controlling variables. Significant and positive relationships between the aggregated urban growth pattern index and air pollution were observed in Northeast China, northern coastal China, and Northwest China, indicating that a high degree of urban aggregation is associated with poor air quality. However, a negative parameter was obtained in southern coastal China, showing an opposite association on urban aggregation and air quality. Nonsignificant connections among the other four zones were found. The findings also highlighted that land use mix, population density, and city size exerted varied and significant influence on air quality across eight economic zones. Overall, this study indicated that understanding the quantitative relationships between urban forms and air quality can provide policymakers with alternative ways to improve air quality in rapidly developing China.

scholarly journals Spatial Measures of Urban Systems: from Entropy to Fractal Dimension

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 991 ◽  
Author(s):  
Yanguang Chen ◽  
Linshan Huang
Keyword(s):  
Fractal Dimension ◽  
Spatial Analysis ◽  
Fractal Dimensions ◽  
Scale Dependence ◽  
Urban Systems ◽  
Scale Free ◽  
Spatial Entropy ◽  
Spatial Systems ◽  
Urban Patterns ◽  
Generalized Entropies

One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurements into fractal dimensions for the spatial analysis of scale-free urban phenomena using the ideas from scaling. Urban systems proved to be random prefractal and multifractal systems. The spatial entropy of fractal cities bears two properties. One is the scale dependence: the entropy values of urban systems always depend on the linear scales of spatial measurement. The other is entropy conservation: different fractal parts bear the same entropy value. Thus, entropy cannot reflect the simple rules of urban processes and the spatial heterogeneity of urban patterns. If we convert the generalized entropies into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. Especially, the geographical analyses of urban evolution can be simplified. This study may be helpful for students in describing and explaining the spatial complexity of urban evolution.

scholarly journals Neighbourhood [Re] Formation: Envisioning A Future For Don Mills

2021 ◽  
Author(s):  
Talayeh Rad
Keyword(s):  
Case Studies ◽  
Urban Growth ◽  
Urban Form ◽  
Urban Morphology ◽  
Recent History ◽  
Design Project ◽  
The Future ◽  
Unlimited Growth ◽  
New Vision ◽  
Future Growth

Architecture is known to be the physical language of community. What define cities are streets, blocks, and buildings, and their interaction defines the neighbourhoods. Cities are poised for unlimited growth (Lefebvre, 2003) and the challenge is to propose a vision for the future growth of already dense neighbourhoods. The research aims to study the evolution of contemporary urbanism, ideas, and theories in order to explore the structure of the existing neighbourhoods and understand the dynamic behind the street patterns and urban blocks. Case studies are investigating the quality and configuration of physical urban form through recent history. The ideas are compared and contrasted to challenge modern and post-modern urban theories in order to propose a new vision for future urban growth. The design project takes into account the importance of urban morphology and typology and their impacts on the identity, diversity and affordability of the neighbourhood.

Modeling Urban Systems

2012 ◽  
pp. 322-351 ◽  
Author(s):  
John D. Landis
Keyword(s):  
Land Use ◽  
Urban Growth ◽  
Travel Behavior ◽  
Growth Models ◽  
Urban Systems ◽  
Economic Base ◽  
Hedonic Price ◽  
Hedonic Price Models ◽  
Different Types ◽  
Behavior Models

This article examines the different types of urban model used in urban planning in North America, and to a lesser extent, in Europe, Asia, and South Americam, which include the population-projection models, economic base models, hedonic price models, and travel-behavior models. It describes emerging procedures such as land-use change and urban-growth models, and looks at Charles Tiebout's model of efficient public choice and Thomas Schelling's model of spatial segregation.

Analysis and Research on Fractal Model of Normal Contact Stiffness of Joint Interfaces

2011 ◽  
Vol 328-330 ◽  
pp. 336-345
Author(s):  
Guo Sheng Lan ◽  
Xue Liang Zhang ◽  
Hong Qin Ding ◽  
Shu Hua Wen ◽  
Zhong Yang Zhang
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Normal Load ◽  
Contact Stiffness ◽  
Fractal Model ◽  
Normal Contact ◽  
Fractal Models ◽  
Normal Contact Stiffness

Through the analysis and research on three fractal models of normal contact stiffness of joint interfaces, the differences between them can be found. Furthermore, numerical simulation was carried out to obtain the complicated nonlinear relations between normal contact stiffness and the normal load. The results show that the normal contact stiffness increases with the normal load, decreases with G but complicatedly varies with D. According to different fractal dimension, we can chose an appropriate one among the three fractal models of normal contact stiffness of joint interfaces when describing normal contact stiffness of joint interfaces.

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