Allometric relations between structural fractal dimensions of road networks and urban quantities

Road infrastructure is one of most important elements in cities. This chapter explores potential allometric relations between the structural fractal dimension (i.e., an index describing the structural complexity of irregular objects) of road networks and various urban quantities (e.g., population, carbon dioxide emissions, and gross domestic product) in Hong Kong for the period from 1971 to 2011. Experimental results show that structural fractal dimension has positive allometric relations with population, carbon dioxide emissions, gross domestic product, merchandise imports, and merchandise exports (with scaling exponents of 1.581, 4.298, 11.113, 13.951, and 14.141, respectively). In addition, inverse allometric relations are discovered with the areas of arable and agricultural land (with scaling exponents of –2.857 and –1.918). These discoveries may provide a new perspective to study urban development.