Urban Allometric Scaling Beneath Structural Fractality of Road Networks

Allometry originally referred to the scaling relationship between the size of a body part and the size of the whole body when an organism grows. Gradually, researchers introduced it into urban studies. In existing urban studies, many allometric relations were discovered, especially those between urban population and other (physical or socioeconomic) quantities, such as urban area and gross domestic product (GDP). Recently, geometric fractal dimension (Dg) was used as a complexity measure of road networks and a linear relationship between Dg and urban population was found. The complexity of a road network is related not only to its geometric form, which can be described by Dg, but also to its topological structure, which can be described by structural fractal dimension (Ds). Whether some relations, such as allometric relations, exist between Ds and other urban quantities is vague. This study explores the allometric relations between the Ds of urban road networks and urban quantities in Hong Kong for the period from 1971 to 2011. It is found that Ds has positive allometric relations with population, CO2 emissions, GDP, merchandise imports, and merchandise exports (with scaling exponents of 1.581, 4.298, 11.113, 13.951, and 14.141, respectively) but inverse allometric relations with the areas of arable and agricultural land (with scaling exponents of −2.857 and −1.918, respectively). These findings indicate that Ds not only has allometric relations with urban quantities but also could have different types of relations. These discoveries could form another basis for the study of urban development.