Fractal dimension study of urban morphology based on network accessibility
ZHANG Chenming1,, GAO Jianhua1,2,, LI Shimin1,3, GAO Shang4, ZHAO Jibin1
1. College of Environment and Planning, Henan University, Kaifeng 475004, Henan, China
2. Key Research Institute of Yellow River Civilization and Sustainable Development, Henan University, Kaifeng 475001, Henan, China
3. Henan Academy of Agricultural Science, Zhengzhou 450002, China
4. College of Tourism and Environment, Shaanxi Normal University, Xi'an 710119, China
In order to expand the range of fractal dimension from the two-dimensional homogeneous space to a composite space integrated with urban land and road network, a network-based calculation method was proposed. Compared with the area-radius method, this new method can clarify the convergence and decentralization of build-up area in the road network rather than in a flat space, which can describe the urban form more reasonably. Fractal dimension of different plots in Zhengzhou downtown area was calculated by applying the above methods. The main conclusions can be summarized as follows: (1) There exists a stable change of the land use density from center to periphery, which meets the requirements of the two fractal models. This means that the land-use system presented a specific fractal feature. (2) The same principles and features for the dimension values have been presented by using two different quantization methods: commercial land < all the construction land (without street and transportation area) < residential land < industrial land. This indicates that the central area in Zhengzhou demonstrated a circle-layer structure and different land-use patterns dominated different layers. The phenomenon can be explained by the land rent theory and affected by the fixed features, such as rivers and railway. (3) The scale-free range determined in the network-based calculation method was larger compared with the traditional area-radius method, which means that the space can be divided more delicately by the scale units constructed in the network-based method. However, the space area corresponding to the scale-free range determined in the new method was smaller. (4) There exist some differences on the dimension values between the above two methods for the same land use type. The results with the network-based method had a dispersive, agglomerate and unremarkable correction function on residential land, commercial land and industrial land respectively compared with the traditional area-radius method.
Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes. Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. "The Fractal Geometry of Nature" is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.
长度一半径维数模型作为描述城市交通网络复杂不确定性现象的一种分形分维方法，其自身存在的不确定性往往被忽视，且相关研究更是鲜见报道。故针对该模型在分形维数测算全过程中存在的不确定性问题，本文率先开展了系统剖析、定量估计和质量控制研究。首先对数据源、矢量化处理、测算中心、尺度选择、以及分维数模型估计等一系列环节进行了不确定性估计与分析，其中首次给出了分形维数在一定置信水平下的不确定性度量区间，并依据误差传播理论对误差的传递和累积进行了描述；然后着重提出了基于LMedS（Least Median of Squares）的质量控制方法。最后通过对拉萨市的算例实验表明：道路的矢量化过程、测算中心和测算尺度的选择都会导致分维的不确定性；并在对数据质量进行控制的基础上，通过置信区间对长度．半径维数模型的不确定性进行了在一定概率水平下的首次度量；同时结合区域现状对研究结果给出了合乎实际的解释。本文在描述表征不确定性问题的分形几何和分形维数的基础上，系统地揭示了其自身不确定性的本质，不仅进一步丰富了分形分维理论，为控制其质量奠定理论基础，而且可为城市交通网络分形维数的地学应用提供可靠的科学依据。
Construction of road infrastructure is a fundamental aspect of the city operation and development, as well as an important pathway and focus to realize the physical urban-rural integration. The long period implementation of "ring + radiation" road system in Beijing has brought a major impact on its urban infrastructure construction and its time accessibility. Particularly in recent years, the rapid increase of private cars in Beijing has become a greater burden to its road system, which has in turn seriously hampered the urban commuting efficiency and added the costs to people's lives. To deal with such challenges and enhance the frog-leap development of transport infrastructure, Beijing has speeded up its development pace in light railway construction since 2008, so as to improve its commuting capacity. This paper tries to measure the time accessibility and its spatial characteristics in the urban areas of Beijing by applying a combined method of vector and raster attribute data generated from major roads and rail transport infrastructure. By using a dual index of accessibility and road density, the paper further reveals the features of spatial accessibility and construction of road systems in the urban areas of the capital, as well as their different presences in the northern and southern parts of the city. The findings of this paper could provide a scientific basis for future urban planning and road system construction for Beijing Municipality.
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Fractal geometry is a new approach for the study of spatial distributions The basic model is a law of hierarchical distribution corresponding to Pareto's law which is familiar to urban geographers and demographers. The methods of fractal analysis can be used to study the spatial organization of human activities across scales. The regularities and the discontinuities in the distributions can then be identified. These discontinuities can be spatially situated. Applying this concept to urbanized areas has shown that districts can be defined and classified according to their scaling relations, thereby allowing development of a typology of locational patterns. This observation reveals the existence of a principle of self-similarity in land-use patterns. An examination of time series shows that despite the apparent fragmentation of these urban tissues, urbanization is often accompanied by self-structuring development. Subsequent research will need to employ complementary morphological measures, such as measures of space filling and of population distribution, which could be used to validate the simulation models based on fractal geometry.