Fractal dimensions of metropolitan area road networks and the impacts on the urban built environment

The fractal dimension of road networks emerges as a measure of the complexity of road transport infrastructures. In this study, we measured fractal dimensions of both the geometric form (i.e., the layout of the roads) and structure hierarchy (i.e., the connections among roads) of the major road networks in the largest 95 U.S. metro areas. We explained the causes of the variances in these fractal dimensions, especially the one for structure hierarchy. Further, we hypothesized the impacts of these fractal dimensions on the urban built environment and validated our hypotheses using path analysis. We found that a larger geometric fractal dimension (D_g) shows a more uniform distribution of roads over the metro area, which provides the accessibility to suburban areas and incentives to low-density development. A larger structural fractal dimension (D_s) indicates the highly-connected roads (e.g., highways) tend to join to other highly-connected roads so that most roads can be reached by a small number of neighboring roads (i.e., the small-world phenomenon). As D_s increases and the small-world effect become more significant, daily vehicle miles traveled per capita (DVMT/Cap) decline. However, D_s should be kept low in order to reduce the DVMT/Cap as population size increases. We consider that the low D_s can contribute to more mixed, polycentric and more uniform on an urban area-wide basis. Overall, higher D_g and D_s of the major road network in a metro area leads to higher per capita carbon emissions of transport, and lower quality of life as population increases. In the end, we conclude that fractal dimensions can provide valuable insight into the nature of the transportation land use nexus.