Fractal Dimension of a Transportation Network and its Relationship with Urban Growth: A Study of the Dallas-Fort Worth Area

Study on the structural characteristics of China's high-speed railway network and its coordination with economic growth based on Fractal theory

As one of the modern transportation modes, the high-speed railway network system has been a robust part of the comprehensive transportation system in China. An important topic emerges the exploration and optimization of its structural organization and coordinated relationship with the regional development, including urban form, land use, and economy. Therefore, supported by the integration of geographical information system (GIS) and fractal theory, this paper aims to carry out an investigation and discussion on the structural characteristics, including intensity (density), complexity, nonstationarity, and heterogeneity of the high-speed railway network in China (HSRNC) from the perspective of the whole country and specific regions, i.e., urban agglomerations. Moreover, based on the time-series data of network mileage expansion and economic output analysis, this study aims to evaluate and characterize the coordinated relationships between network development and economic growth in the context of the nationwide area and urban agglomerations. This study aims to explore and promote the spatial structural organization and morphology of the high-speed railway network in China, thus improving the coordinated development with the regional economic growth, for giving a new perspective to the future planning and evolution of the high-speed railway network in China.

Exploring Spatial Patterns of Interurban Passenger Flows Using Dual Gravity Models

Geographical gravity models can be employed to quantitatively describe and predict spatial flows, including migration flows, passenger flows, daily commuting flows, etc. However, how to model spatial flows and reveal the structure of urban traffic networks in the case of missing partial data is still a problem to be solved. This paper is devoted to characterizing the interurban passenger flows in the Beijing-Tianjin-Hebei region of China using dual gravity models and Tencent location big data. The method of parameter estimation is the least squares regression. The main results are as follows. First, both the railway and highway passenger flows can be effectively described by dual gravity models. A small part of missing spatial data can be compensated for by predicted values. Second, the fractal properties of traffic flows can be revealed. The railway passenger flows follow the gravity scaling law better than the highway passenger flows. Third, the prediction residuals indicate the changing trend of interurban connections in the study area in recent years. The center of gravity of the spatial dynamics has shifted from the Beijing-Tianjin-Tangshan triangle to the Beijing-Baoding-Shijiazhuang axis. A conclusion can be reached that the dual gravity model is an effective tool for analyzing spatial structures and dynamics of traffic networks and flows. Moreover, the model provides a new approach to estimating the fractal dimensions of traffic networks and spatial flow patterns.

The impact of visual complexity on perceived safety and comfort of the users: A study on urban streetscape of Sri Lanka

Increase in the variety of development in urban context has made it more complicated and complex for the users of public spaces. Absence of sufficient information to read the surrounding causes psychological anxiousness leading to perceived danger or discomfort for the urbanites. Consequently, perceived safety and comfort of the users is distinctively low in urban contexts, creating neglected and underused spaces. Complexity is one of the information processing variables as per Kaplan and Kaplan’s informational model which helps users to comprehend the surrounding environment. The streetscape plays a vital role in the daily movement patterns within the urban cities and is the transition boundary between the public and private realms. Visual complexity of these streets is a result of different configurations of elements within the urban areas. This research is conducted to ascertain the relationship between visual complexity levels of the streets with the perceived safety and comfort of the users. Shannon Diversity Index (SDI) and Fractal dimension analysis were conducted with 48 SVIs (Street View Images) selected within 1km radius of Colpetty junction, Colombo Sri Lanka covering all the possible compositions found within the context. The visual index data extraction had identified ten major components within the selected 48 SVIs. 78 subjective ranking responses for perceived safety, comfort (preference) and perceived complexity were collected from snowball sampling. Findings of the study revealed that perceived safety levels and preference scores for the SVIs are related to the Shannon Diversity Index calculation in an inverted ‘U’ shape where the highest and lowest SDI values are related with low preference scores and low safety levels. The SVIs with medium SDI values are perceived as the safest and most preferred by the users of urban streets of Colombo Sri Lanka. The SDI and fractal dimension values were significantly correlated with the perceived complexity scores of the users. The results of this study can be accommodated in the planning and designing of urban streetscapes of tropical climates for sustainable and friendly urban expansions.

An Overview of Fractal Geometry Applied to Urban Planning

Since computing advances in the last 30 years have allowed automated calculation of fractal dimensions, fractals have been established as ubiquitous signatures of urban form and socioeconomic function. Yet, applications of fractal concepts in urban planning have lagged the evolution of technical analysis methods. Through a narrative literature review around a series of “big questions” and automated bibliometric analysis, we offer a primer on fractal applications in urban planning, targeted to urban scholars and participatory planners. We find that developing evidence demonstrates linkages between urban history, planning context, and urban form and between “ideal” fractal dimension values and urban aesthetics. However, we identify gaps in the literature around findings that directly link planning regulations to fractal patterns, from both positive and normative lenses. We also find an increasing trend of most literature on fractals in planning being published outside of planning. We hypothesize that this trend results from communication gaps between technical analysts and applied planners, and hope that our overview will help to bridge that gap.

Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou, China: 1964–2010

Urban population density provides a good perspective for understanding urban growth and socio-spatial dynamics. Based on sub-district data of the five national censuses in 1964, 1982, 1990, 2000, and 2010, this paper is devoted to analyzing of urban growth and the spatial restructuring of the population in the city of Hangzhou, China. Research methods are based on mathematical modeling and field investigation. The modeling result shows that the negative exponential function and the power-exponential function can be well fitted to Hangzhou’s observational data of urban density. The negative exponential model reflects the expected state, while the power-exponential model reflects the real state of urban density distribution. The parameters of these models are linearly correlated to the spatial information entropy of population distribution. The fact that the density gradient in the negative exponential function flattened in the 1990s and 2000s is closely related to the development of suburbanization. In terms of investigation materials and the changing trend of model parameters, we can reveal the spatio-temporal features of Hangzhou’s urban growth. The main conclusions can be reached as follows. The policy of reformation and opening-up and the establishment of a market economy improved the development mode of Hangzhou. As long as a city has a good social and economic environment, it will automatically tend to the optimal state through self-organization.

Geospatial Assessment of the Territorial Road Network by Fractal Method

This paper proposes an approach to the geospatial assessment of a territorial road network based on the fractals theory. This approach allows us to obtain quantitative values of spatial complexity for any transport network and, in contrast to the classical indicators of the transport provisions of a territory (Botcher, Henkel, Engel, Goltz, Uspensky, etc.), consider only the complexity level of the network itself, regardless of the area of the territory. The degree of complexity is measured by a fractal dimension. A method for calculating the fractal dimension based on a combination of box counting and GIS analysis is proposed. We created a geoprocessing script tool for the GIS software system ESRI ArcGIS 10.7, and a study of the spatial pattern of the transport network of the Ukraine territory, and other countries of the world, was made. The results of the study will help to better understand the different aspects of the development of transport networks, their changes over time and the impact on the socioeconomic indicators of urban development.

Population changes in residential clusters in Japan

Population dynamics in urban and rural areas are different. Understanding factors that contribute to local population changes has various socioeconomic and political implications. In the present study, we use population census data in Japan to examine contributors to the population growth of residential clusters between years 2005 and 2010. The data set covers the entirety of Japan and has a high spatial resolution of 500 × 500 m2, enabling us to examine population dynamics in various parts of the country (urban and rural) using statistical analysis. We found that, in addition to the area, population density, and age, the shape of the cluster and the spatial distribution of inhabitants within the cluster are significantly related to the population growth rate of a residential cluster. Specifically, the population tends to grow if the cluster is "round" shaped (given the area) and the population is concentrated near the center rather than periphery of the cluster. Combination of the present results and analysis framework with other factors that have been omitted in the present study, such as migration, terrain, and transportation infrastructure, will be fruitful.

Climate forcing and infectious disease transmission in urban landscapes: integrating demographic and socioeconomic heterogeneity

Urbanization and climate change are the two major environmental challenges of the 21st century. The dramatic expansion of cities around the world creates new conditions for the spread, surveillance, and control of infectious diseases. In particular, urban growth generates pronounced spatial heterogeneity within cities, which can modulate the effect of climate factors at local spatial scales in large urban environments. Importantly, the interaction between environmental forcing and socioeconomic heterogeneity at local scales remains an open area in infectious disease dynamics, especially for urban landscapes of the developing world. A quantitative and conceptual framework on urban health with a focus on infectious diseases would benefit from integrating aspects of climate forcing, population density, and level of wealth. In this paper, we review what is known about these drivers acting independently and jointly on urban infectious diseases; we then outline elements that are missing and would contribute to building such a framework.

Resilience of Self-Organised and Top-Down Planned Cities--A Case Study on London and Beijing Street Networks

The success or failure of the street network depends on its reliability. In this article, using resilience analysis, the author studies how the shape and appearance of street networks in self-organised and top-down planned cities influences urban transport. Considering London and Beijing as proxies for self-organised and top-down planned cities, the structural properties of London and Beijing networks first are investigated based on their primal and dual representations of planar graphs. The robustness of street networks then is evaluated in primal space and dual space by deactivating road links under random and intentional attack scenarios. The results show that the reliability of London street network differs from that of Beijing, which seems to rely more on its architecture and connectivity. It is found that top-down planned Beijing with its higher average degree in the dual space and assortativity in the primal space is more robust than self-organised London using the measures of maximum and second largest cluster size and network efficiency. The article offers an insight, from a network perspective, into the reliability of street patterns in self-organised and top-down planned city systems.

The Fractal Analysis of Architecture: Calibrating the Box-Counting Method Using Scaling Coefficient and Grid Disposition Variables

Since the mid-1990s architectural researchers have used the box-counting method to calculate the fractal dimension of a range of buildings and urban forms. While this approach has been widely adopted, there has been little consistency in how the multiple variables in the method have been applied. Furthermore, despite precedents in the sciences, no attempt has been made in architectural or urban analysis to use these parameters to calibrate or refine the method. In this paper the computational version of the box-counting approach is presented along with its methodological variables. Thereafter, nine mathematical fractals with known dimensions are tested using this method to identify the optimal approach to the scaling coefficient and grid disposition variables. Finally, using these new settings, two classic architectural test cases are reexamined: Robie House and the Villa Savoye.

Fractal cartography of urban areas

In a world in which the pace of cities is increasing, prompt access to relevant information is crucial to the understanding and regulation of land use and its evolution in time. In spite of this, characterization and regulation of urban areas remains a complex process, requiring expert human intervention, analysis and judgment. Here we carry out a spatio-temporal fractal analysis of a metropolitan area, based on which we develop a model which generates a cartographic representation and classification of built-up areas, identifying (and even predicting) those areas requiring the most proximate planning and regulation. Furthermore, we show how different types of urban areas identified by the model co-evolve with the city, requiring policy regulation to be flexible and adaptive, acting just in time. The algorithmic implementation of the model is applicable to any built-up area and simple enough to pave the way for the automatic classification of urban areas worldwide.