Urban Allometric Scaling Beneath Fractality Of Road Networks

Fractal is the optimized structure of nature and the fourth-generation language of geography.The ubiquitous fractal transportation network in the living body enables the energy in the living body to be transported to all parts of the body to the maximum.Therefore,fractal is also called the "fourth dimension" of life.The law of allometric growth is the "invisible hand" that controls the growth rate and lifespan of living bodies.From cells to cities,the evolution of various complex systems exhibits the law of allometric growth.At present,the research of fractal cities is mostly limited to geometric fractals,and there is not enough attention to structural fractal,especially the lack of structural time fractal,that is,allometric growth research,to a certain extent,limits our understanding of the law of self-organization of urban space.The road network is an important part of the city and the skeleton of the city.This article takes the urban road network as the research object,and aims to excavate the geometric and structural fractal features of the urban road network and reveal the law of allometric growth of the city driven by the fractal.The paper collects road network data and corresponding social and economic indicators such as population,economy,transportation,land use,industry,and scientific research of the top 100 Chinese cities.We calculated the geometric shape and structural characteristics of the urban road network,and analyzed the possible allometric growth correlation between these indicators and each other and between them and the socioeconomic indicators.The research results show that the urban road network is not only a typical geometric fractal,but also a structural fractal.The values of the six fractal dimensions are normally distributed.For the geometric fractal dimension,the values of box-counting dimension,length-radius dimension and branch-radius dimension are [1.181,1.818],[1.157,1.736],[1.153,1.758];For the structural fractal dimension,the value ranges of box-covering structural fractal dimension,volume structure fractal dimension and degree-volume structure fractal dimension are [2.259,3.875],[2.618,4.252],[2.152,3.567].Generally speaking,the volume structure fractal dimension is larger than the box covering structure fractal dimension,which is greater than the volume volume structure fractal dimension.Spatially,cities with high fractal dimension of road network are clustered in the Beijing-Tianjin-Hebei metropolitan area,the Yangtze River Delta and Pearl River Delta regions,and scattered in the central and southwest regions;cities with low fractal dimension Spread everywhere.The results of the study further confirmed the characteristics of the small world,scale-free and structural self-similarity of the urban road network,revealing that there are three types of allometric growth relationship:positive allometric growth relation,negative allometric growth relation and inverse allometric growth relation between the fractal dimension of the road network and the socio-economic indicators.