基于路网可达性的城市空间形态集聚分形研究

为将城市形态分形维数从平面空间拓展到交通网络系统,提出一种基于路网的分形集聚维数测算方法,探讨该维数的集聚—扩散性质。以郑州市中心城区为案例区,分别测算了各类功能用地半径集聚维数和路网集聚维数。结果表明：① 各类用地无论在平面中还是在路网中,密度从中心向外围的变化在特定区间内都是均匀的,符合分形特征。② 两种维数均呈现出商业用地<全部建设用地（不含道路与交通设施用地）<居住用地<工业及仓储用地的规律。③ 对于同类功能用地,相对于半径维数,路网集聚维数标度不变区尺度范围更广,对空间的划分也更为精细。④ 同类用地两种集聚维数的分形测量值存在差异,这体现出路网集聚维数对传统测度结果具有一定的延展—集聚修正作用。

Fractal dimension study of urban morphology based on network accessibility

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.