Multifractal analysis of axial maps applied to the study of urban morphology

Ariza-Villaverde, Ana B.; Jiménez‐Hornero, Francisco J.; Ravé, E. Gutierrez de

doi:10.1016/j.compenvurbsys.2012.11.001

Cited by 71 publications

(52 citation statements)

References 48 publications

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“…Until recently, a single fractal dimension was employed. It is well recognised now, that a spectrum of fractal dimensions needs to be employed to fully characterise systems that present different fractal properties at different scales and regions [15], as is the case of urban systems [16][17][18]. These systems are called multifractals.…”

Section: Introductionmentioning

confidence: 99%

Multifractal to monofractal evolution of the London street network

et al. 2015

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We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not suffice to capture the dynamics of the system. Instead, for a proper characterization of such a dynamics, the multifractal spectrum needs to be considered. Our analysis reveals that London evolves from an inhomogeneous fractal structure, that can be described in terms of a multifractal, to a homogeneous one, that converges to monofractality. We argue that London's multifractal to monofracal evolution might be a special outcome of the constraint imposed on its growth by a green belt. Through a series of simulations, we show that multifractal objects, constructed through diffusion limited aggregation, evolve towards monofractality if their growth is constrained by a non-permeable boundary.

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Section: Introductionmentioning

confidence: 99%

Multifractal to monofractal evolution of the London street network

et al. 2015

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“…The cluster is formed if they satisfy Formula (15) and no new object is added to the cluster, thus identifying them as clustered. 3 Traverse all points that are not clustered by iterating operations (1)- (2). When clustering is finished, any point that does not belong to a cluster will be identified as noise.…”

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confidence: 99%

Building an Urban Spatial Structure from Urban Land Use Data: An Example Using Automated Recognition of the City Centre

Zhu

Sun

2017

IJGI

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It has been suggested that the method of constructing an urban spatial structure typically follows a forward process from planning and design up to expression, as reflected in both graphic and text descriptions of urban planning. Although unorthodox, the original status structures can be extracted and constructed from an existing urban land-use map. This approach not only provides the methodological foundation for urban spatial structure evolution and allows for a comparative and quantitative analysis between the existing and planned conditions, but also lays a theoretical basis for failure in scientific decision making during the planning phase. This study attempts to achieve this by identifying the city centre (a typical element of the urban spatial structure) from urban land use data. The city centre is a special region consisting of several units with particular spatial information, including geometric attributes, topological attributes, and thematic attributes. In this paper, we develop a methodology to support the delineation of the city centre, considering these factors. First, using commercial land data, we characterise the city centre as units based on a series of indicators, including geometric and thematic attributes, and integrate them into a composite index of "urban centrality"; Second, a graph-based spatial clustering method that considers both topological proximity and attribute similarity is designed and used to identify the city centre. The precise boundary of the city centre is subsequently delimited using a shape reconstruction method based on the cluster results. Finally, we present a case study to demonstrate the effectiveness and practicability of the methodology.

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“…As mentioned above, besides box-counting method, the common methods leading to the fractal dimension of urban area include area-radius scaling, density-radius scaling, sandbox method, and wave spectrum scaling. Among these methods, sandbox is a good approach to calculate multifractal parameters [61], and maybe this method can be employed to research entropy and fractal dimension from a new angle of view. Third, multifractal parameters based on Renyi entropy is not discussed in depth.…”

Section: Discussionmentioning

confidence: 99%

Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy

Chen

Wang

Feng

2017

Entropy

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Abstract:The 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 and reflect the local features of random multi-scaling structure. 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, capacity dimension, information dimension, and correlation dimension, are utilized to make empirical analyses of the urban form of two Chinese cities, Beijing and Hangzhou. The results show that the entropy values vary with the measurement scale, but the fractal dimension value is stable is method and study area are fixed; if the linear size of boxes is small enough (e.g., <1/25), the linear correlation between entropy and fractal dimension is significant (based on the confidence level of 99%). Further empirical analysis indicates that fractal dimension is close to the characteristic values of spatial entropy. This suggests that the physical meaning of fractal dimension can be interpreted by the ideas from entropy and scaling and the conclusion is revealing for future spatial analysis of cities.

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Multifractal analysis of axial maps applied to the study of urban morphology

Cited by 71 publications

References 48 publications

Multifractal to monofractal evolution of the London street network

Multifractal to monofractal evolution of the London street network

Building an Urban Spatial Structure from Urban Land Use Data: An Example Using Automated Recognition of the City Centre

Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy

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