Exploring the Structural Fractality of Urban Road Networks by Different Representations

Organisms and other living things grow as fractals, helping to maximize space-filling ability and transmit flow efficiently. In recent years, many studies on fractals have been carried out, mostly at a geometric level, although little work has been done on fractal properties at a structural level. In fact, the capacity of geographical objects, especially road networks, is dependent not only on the geometric distribution described by a geometric fractal dimension but also on the level of structural complexity as described by a structural fractal dimension. Past studies on a structural fractal dimension are limited to a single scale and a single representation. Because different representations could lead to different results in fractal analysis, this study aims to examine the structural fractality of urban road networks by different representations. The road networks of the 100 most populous cities in the United States were examined by three commonly used topological representations. The following results were established: Despite differences in representation, structural fractality always exists; structural fractal dimensions in stroke-based representation are obviously larger than those in segment-based representation; and scale has no obvious effects on structural fractality. These results could deepen our understanding of how urban road networks evolve.