  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.
