Fractal dimension of a transportation network and its relationship with urban growth: a study of the Dallas - Fort Worth area

A city and its transportation network are both complicated systems. Fractal geometry provides an effective way to describe the complex property of geographical features. This paper uses a modified box-counting method to describe the fractal property of urban transportation networks. Assuming that human settlements of different sizes are all operated by the same growth procedure, this paper investigates the relationship between the mass size of cities and the complexity of their road systems. The results confirm that, as cities grow from small to large, their transportation networks generally become more complicated -- the urban spaces are filled up more densely by city roads and the locations within a city are more accessible. The quantitative relationship identified between the complexity of urban transportation network and city size provides an empirical guide for the planning and policymaking of urban development and road construction.