Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing, P.R.China.
PLoS One. 2021 Feb 18;16(2):e0246925. doi: 10.1371/journal.pone.0246925. eCollection 2021.
Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifractal parameters. The results showed multifractal structure of urban street networks. The global multifractal dimension spectrums are inverse S-shaped curves, while the local singularity spectrums are asymmetric unimodal curves. If the moment order q approaches negative infinity, the generalized correlation dimension will seriously exceed the embedding space dimension 2, and the local fractal dimension curve displays an abnormal decrease for most cities. The scaling relation of local fractal dimension gradually breaks if the q value is too high, but the different levels of the network always keep the scaling reflecting singularity exponent. The main conclusions are as follows. First, urban street networks follow multifractal scaling law, and scaling precedes local fractal structure. Second, the patterns of traffic networks take on characteristics of spatial concentration, but they also show the implied trend of spatial deconcentration. Third, the development space of central area and network intensive areas is limited, while the fringe zone and network sparse areas show the phenomenon of disordered evolution. This work may be revealing for understanding and further research on complex spatial networks by using multifractal theory.
交通网络已被证明是分形系统。然而，以前的研究主要集中在单分形网络上，而复杂系统具有多分形结构。本文致力于探索 12 个中国城市街道网络中多分形标度过程的一般规律。采用城市聚类算法识别城市边界，以定义可比的研究区域；采用盒子计数法和直接确定法提取空间数据；采用最小二乘法计算全局和局部多分形参数。结果表明城市街道网络具有多分形结构。全局多分形维谱呈倒 S 形曲线，而局部奇异谱呈不对称单峰曲线。当阶数 q 接近负无穷大时，广义关联维数将严重超过嵌入空间维数 2，并且大多数城市的局部分形维数曲线显示出异常下降。如果 q 值过高，局部分形维数的标度关系将逐渐破坏，但网络的不同层次始终保持反映奇异指数的标度。主要结论如下。首先，城市街道网络遵循多分形标度规律，标度先于局部分形结构。其次，交通网络的模式呈现出空间集中的特征，但也表现出空间分散的隐含趋势。第三，中心区和网络密集区的发展空间有限，而边缘区和网络稀疏区则表现出无序演化的现象。这项工作可能有助于通过使用多分形理论理解和进一步研究复杂的空间网络。
