A Comparison Between Two Ols-Based Approaches to Estimating Urban Multifractal Parameters

Huang, Linshan; Chen, Yanguang

doi:10.1142/s0218348x18500196

Cited by 18 publications

(19 citation statements)

References 39 publications

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“…Basic mathematical analysis. Further, all parameter values to the global indicators and local indicators in three spatial scales (m = 5 (block level), m = 6 (road level), m = 7 (life cell level)) in the four years are obtained using a standardized mathematical analysis program (Huang and Chen, 2018). In addition, the corresponding mathematical features were interpreted according to factors such as the size of each parameter value, the shape of the fitting curve, and the size of the goodness of fit (R 2 ) and were used as the basis for the mathematical analysis of global and local indicators.…”

Section: Case Studymentioning

confidence: 99%

Multifractal features of spatial variation in construction land in Beijing (1985–2015)

Song

2019

Palgrave Commun

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Over the last 30 years, Beijing has experienced rapid development. The city's spatial pattern and changes are extremely complicated. Therefore, to reveal the spatial patterns at different scales and levels, the construction land in Beijing within the 6th ring road in 1985, 1999, 2008, and 2015, was analyzed using global and local multifractal analyses. The global analysis shows that, over the past 30 years, the development of new construction land in this region experienced a process that transformed it from being a hierarchical spatial structure with a low-evolution intensity (1985) to being a spatial structure with a higher evolution intensity and multi-scale differential development (1999, 2008) with a hierarchical spatial system (one main urban area with a number of satellite towns) (2015). Local analysis further shows that the spatial pattern of the construction land in this region tended to be simplified over the past 30 years. The construction land in this region displays specific evolutionary characteristics with the increase in breadth (q) and intensity (D q ) and a multifractal dimension spectrum (f(a) -a(q)) and dominant spectrum at various spatial scales over a four-year period. In general, the influence of high-density areas on the spatial pattern of the construction land is decreasing, while the influence of low-density areas is increasing. Based on this, this paper also summarizes the theoretical value of multifractal analysis in economic geography research, highlighting its advantages, limitations, and application range, and presents the technical analysis process and other suggestions for future research.

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Section: Case Studymentioning

confidence: 99%

Multifractal features of spatial variation in construction land in Beijing (1985–2015)

Song

2019

Palgrave Commun

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“…The datasets came from the remote sensing images of four years, that is, 1984, 1994, 2006, and 2015 ( Figure 3 ). A number of thematic mapper (TM) images of Landsat with a ground resolution of 30 meters of Beijing from the National Aeronautics and Space Administration (NASA) (1984, 1994, 2006) and Institute of Remote Sensing and Digital Earth (ISDE) of the Chinese Academy of Sciences (CAS) (2015) are available for spatial analysis [ 29 , 34 ]. The functional box-counting method can be employed to measure the Renyi entropy and calculate multifractal parameters.…”

Section: Empirical Analysismentioning

confidence: 99%

“…Using a linear regression technique, we can estimate the generalized correlation dimension D q , which is just the slope of the semi-logarithmic equation. It should be noted that the regression equation has no intercept [ 34 ]. If q = 1, Equations (4) and (5) will be invalid.…”

Section: Empirical Analysismentioning

confidence: 99%

“…The above process of data extraction and parameter estimation is convenient by means of ArcGIS technique and mathematical computation software such as Matlab. The methods and steps have been illustrated in previous works [ 29 , 34 ]. Partial spatial Renyi entropy values for Beijing are shown in Table 3 , and the corresponding multifractal parameters are displayed in Table 4 .…”

Section: Empirical Analysismentioning

confidence: 99%

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Spatial Measures of Urban Systems: from Entropy to Fractal Dimension

Chen

Huang

2018

Entropy

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A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between entropy and fractal dimension, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurement into fractal dimension for the spatial analysis of scale-free urban phenomena using ideas from scaling. Urban systems proved to be random prefractal and multifractals systems. The entropy of fractal cities bears two typical properties. One is the scale dependence. Entropy values of urban systems always depend on the scales of spatial measurement.The other is entropy conservation. Different fractal parts bear the same entropy value. Thus entropy cannot reflect the spatial heterogeneity of fractal cities in theory. If we convert the generalized entropy into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. The essence of scale dependence is the scaling in cities, and the spatial heterogeneity of cities can be characterized by multifractal scaling. This study may be helpful for the students to describe and understand spatial complexity of cities.

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“…In 2013, Chen and Wang studied the multifractal spectrums of Beijing's the spatio-temporal development indicates the city's spatial structure can be loosely divided into three layers from the downtown to its suburban, i.e., (1) City centre-due to overfilling of space, the fractal structure of highdensity regions is degenerated; (2)Suburban-due to the spatial constraint of urban growth, the scaling properties of the lowdensity regions become disordered;(3) the change extents of fractal parameters become narrower with the passage of time as the city is filled to capacity (Chen and Wang 2013). In 2018, Huang and Chen's paper has compared two ordinary least squares (OLS)-based approaches for estimating urban multifractal parameters (Huang and Chen, 2018). In particular, significant changes have taken place in the industrial structure of Beijing's suburban areas, and these changes directly impact the micro-and meso-scale evolution of these areas.…”

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confidence: 99%

Spatio-temporal evolutionary analysis of the township enterprises of Beijing suburbs using computational intelligence assisted design framework

et al. 2018

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Township and village enterprises (TVEs) are market-oriented public enterprises under the purview of local governments based on townships and villages in the People's Republic of China. TVEs have become a vibrant part of the Chinese economy following the significant expansion during the 1980s reform period. In the mid-2000s, TVEs became an integrated part of Chinese industry after the property rights transition. In this study, we examined the dynamic behaviours of TVEs in the near-inner-outer suburbs; we simulated these behaviours using computational intelligence aided design framework, which embedded the micro-genetic algorithm with variable populations (VPμGA). Specifically, we assume that conditions follow development, which includes industry scale, industry profit, employees and district development; we then utilise the VPμGA method to simulate the industrial structure and spatio-temporal evolution of the TVEs across seven industrial sectors and closely analyse the consequences of the transition. Our analysis results are consistent with actual observations, and a macro-level analysis showed that TVEs experienced defined scenarios. For Beijing, these scenarios are as follows: rapid development → chaotic development → steady development. The micro-level analysis showed that TVEs and labour have gradually formed a specific industry, a complex trend that evolved in both space and time. We determined the dynamic behaviours of the structures at micro-scales, meso-scales and macro-scales, clarifying the development of TVEs in the Beijing suburbs.

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A Comparison Between Two Ols-Based Approaches to Estimating Urban Multifractal Parameters

Cited by 18 publications

References 39 publications

Multifractal features of spatial variation in construction land in Beijing (1985–2015)

Multifractal features of spatial variation in construction land in Beijing (1985–2015)

Spatial Measures of Urban Systems: from Entropy to Fractal Dimension

Spatio-temporal evolutionary analysis of the township enterprises of Beijing suburbs using computational intelligence assisted design framework

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