Understanding Fractal Dimension of Urban Form through Spatial Entropy

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 linear correlation between entropy and fractal dimension is clear. 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 scales and the conclusion is revealing for future spatial analysis of cities. Key words: fractal dimension; entropy; mutlifractals; scaling; urban form; Chinese citiesComment: 26 pages, 7 figures, 8 table

: FRACTALOPOLIS MODEL - ACCESSIBILITY, EVALUATION & MORPHOLOGICAL RULES

page number: 74A sustainable and sustaining planning strategy is globally important for metropolitan areas. Sustainable planning addresses the development of strategies to reduce the use of resources, increase economic efficiency and improve integration of social aspects. In contrast, splinter development (e.g. urban sprawl) involves damage to nature and generation of an increasing volume of traffic (these are the main criticisms following a study by Newman and Kenworthy (1989) on the relationship between settlement density and energy consumption). Interestingly, the overly compact city also has this effect as it may generate traffic flows for accessing green and leisure areas, or changes of residence due to a favouring of sites that lie farther away from the centre than the inhabitants' current places of residence. Households not only consume urban amenities integrated into densely populated areas, but also aspire to have access to green and leisure areas. Schwanen et al. (2004) showed that households usually optimize their residential choice with respect to accessibility to various types of amenities, which is inherently linked to the frequentation rate of these amenities (daily, weekly, monthly, and occasional) (c.f. spatial practice of people). Moreover, on an urban scale, over-compactness causes ecological problems such as a lack of green wedges for supplying the city with fresh air (urban microclimate). Thus, we aim to find a solution for managing dispersed development which marries the twin elements of green and built-up space in a highly efficient manner. This solution also needs to incorporate dynamic aspects of a city as well as minimizing traffic costs and emissions. Based on the observation that urban space is founded on the principle of fractal geometry, it seems interesting to explore to what extent fractal geometry may be drawn upon for solving the spatial antagonism of compactness and urban sprawl.Une stratégie d'aménagement durable représente un enjeu important pour le développement des agglomérations contemporaines. L'aménagement durable implique le développement de stratégies visant à réduire l'utilisation des ressources, accroître l'efficacité économique et améliorer l'intégration des aspects sociaux (ex. environnements conviviaux pour les piétons, équilibre entre modes de transport public/privé, réseaux routiers performants, viabilisation des terres agricoles, économie du mouvement ; accès à l'emploi pour tous, commerces, services ; santé, culture et loisirs). A l'inverse, le développement fractal (ex. étalement urbain) n'est pas sans répercussions néfastes sur la nature et tend à augmenter le volume du trafic (principales critiques émises dans une étude de Newman & Kenworthy, 1989, portant sur les relations entre densité d'implantation et consommation d'énergie). Fait intéressant, une ville trop compacte induit un effet semblable car elle peut être à l'origine de flux de trafic pour accéder aux espaces verts et récréatifs ou des déménagements vers des endroits plus éloignés du centre que les lieux de résidence actuels des citadins. Les ménages ne se contentent pas d'utiliser les aménagements urbains intégrés dans les zones à forte densité de population, ils aspirent également à un accès aux espaces verts et récréatifs. Schwanen et al. (2004) ont mis en évidence le fait que les ménages tendaient à optimiser leur choix de résidence en fonction de l'accessibilité de divers types de commodités, un phénomène foncièrement lié au taux de fréquentation (quotidienne, hebdomadaire, mensuelle et occasionnelle) de ces dernières (cf. pratiques spatiales de la population). A l'échelle urbaine, une compacité excessive entraîne par ailleurs des problèmes écologiques, tels que le manque d'espaces verts pour approvisionner la ville en air frais (microclimat urbain). Nous recherchons ainsi une solution afin de gérer le développement fractal de manière à pouvoir concilier efficacement le couple antinomique espaces verts/espaces urbanisés. Cette solution doit également intégrer les aspects dynamiques d'une ville et minimiser les émissions et les coûts du trafic et prévenir la désagrégation des terres agricoles. Sur la base de l'observation selon laquelle l'espace urbain repose sur le principe de la géométrie fractale, il paraît intéressant d'explorer dans quelle mesure la géométrie fractale peut être mise à contribution en vue de résoudre l'antagonisme spatial compacité/étalement urbain

A simulation-based approach to assess impacts of urban logistics policies on traffic flow dynamics

International audienceIn urban environments, there are now many challenging problems concerning freight transport.As cities around the world grow rapidly, there is an increase in pickup-delivery truck traffic inurban areas. It turns out that commercial traffic is now a major source of externalities in metroareas, including congestion, noise, air pollution (small particulates, NOx, greenhouse gasemissions), and traffic incidents [1].To overcome these issues, many interesting and innovative strategies have been developed inEurope and other parts of the world. Especially, some researchers proposed the idea of citylogistics to solve these difficult problems [2-3]. The idea of this concept is to rationalize thefreight activities in cities by optimizing operations considering the traffic conditions and thecongestion issues. Consequently, public authorities strongly need decision support frameworksto evaluate urban logistics planning and management.It turns out that a key point in predicting the impacts of city logistics is the influence of freighton traffic flow dynamics. Particularly, pickup-delivery trucks maneuvers generate roadcapacity reduction and lead to delay for individual drivers. Although this is a crucial topic, theliterature rarely addresses this issue. This paper aims to fill this lack of understanding byincorporating the effects of urban freight in a traffic flow model

Modelling the interdependence of spatial scales in urban systems

The multitude of interwoven spatial scales and their relevance for urban systems has been of interest to the complexity science of cities since its conception. Today, we are well aware that urban environments are being simultaneously shaped and organised through actions at all levels. However, the fundamental question of how to reveal and quantify the interdependence of processes in between various spatial and temporal scales is less often addressed. Deepening our theoretical understanding of the multiscale spatiotemporal complexity of urban systems demands a transdisciplinary framework and the deployment of novel and advanced mathematical models. This article performs a multiscale analysis of urban structures using a large dataset of rent price values in the Ruhr area, Germany. We argue that, due to their many interacting degrees of freedom, urban systems exhibit similar features as other strongly correlated systems, for example, turbulent flows, notably the occurrence of extreme small-scale fluctuations. This analogy between urban and turbulent systems, which we support by empirical evidence, allows for the modelling of spatial structures on the basis of concepts and methods from turbulence theory. We demonstrate how by identifying the main turbulence-borrowed characteristics of an arbitrary two-dimensional urban field, it can be fully reproduced with a small number of prescribed points. Our findings have theoretical implications in the way we quantify and analyse scales in urban systems, model small-scale urban structures as well as potential policy relevance on understanding the evolution and spatial organisation of cities