论文标题
城市街道网络结构的多重尺度缩放分析：中国十二个大城市的案例
Multifractal scaling analyses of urban street network structure: the cases of twelve megacities in China
论文作者
论文摘要
交通网络已被证明是分形系统。但是，先前的研究主要集中在单一网络上，而复杂的系统则具有多重分子结构。本文致力于探索12个中国城市的街头网络中多重缩放过程的一般规律性。使用城市聚类算法来确定定义可比研究领域的城市边界；使用盒子计数法和直接确定方法用于提取空间数据；最小二乘计算用于估计全局和局部多重分数参数。结果表明，城市街道网络的多重结构。全局多重尺寸光谱是逆S形曲线，而局部奇异性光谱是不对称的单峰曲线。如果Moment Order Q接近负无穷大，则广义相关维度将严重超过嵌入式空间维度2，而局部分形维度曲线在大多数城市中显示出异常下降。如果Q值太高，则局部分形维度的缩放关系会逐渐破坏，但是网络的不同级别始终保持缩放反映奇异性指数。主要结论如下。首先，Urban Street网络遵循多重规模定律，并在当地分形结构之前进行缩放。其次，交通网络的模式具有空间浓度的特征，但它们也显示了空间解浓度的隐含趋势。第三，中央区域和网络密集型区域的发展空间有限，而边缘区和网络稀疏区域显示了进化不足的现象。这项工作可能揭示了通过使用多重分子理论对复杂空间网络的理解和进一步研究。
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.
