Perfusion and urban thickness: The shape of cities

The Science of Cities seeks to understand how urban areas function in an effort to shape sustainable and equitable development. This research introduces the concept of perfusion dynamics as an underpinning theory to explain urban growth. We suggest that there is a maximum distance from the urban edge beyond which goods and services no longer evenly permeate interior urban neighborhoods. We draw from concepts of perfusion in the biological and ecological sciences for support. Reconsidering urban form with perfusion dynamics helps explain the fractal, branching pattern of urban growth and dynamics at play in studies on urban scale. To provide proof of concept, we demonstrate how to measure the urban thickness with geoprocessing tools using a dataset of 13,561 Urban Areas in the United States. We show that as urban areas approach a threshold of 10 km in thickness, they tend to elongate. Over a third of US urban areas are within 0.5 km of the urban interface. Only 4% of all urban areas have grown beyond the perfusion constraint of 5 km from the urban interface. Because the urban interface is socially governed, our exploratory research points out practical considerations for urban planning and future research.