Universal scaling of the distribution of land in urban areas

In this work, we explore the spatial structure of built zones and green areas in diverse western cities by analyzing the probability distribution of areas and a coefficient that characterize their respective shapes. From the analysis of diverse datasets describing land lots in urban areas, we found that the distribution of built-up areas and natural zones in cities obey inverse power laws with a similar scaling for the cities explored. On the other hand, by studying the distribution of shapes of lots in urban regions, we are able to detect global differences in the spatial structure of the distribution of land. Our findings introduce information about spatial patterns that emerge in the structure of urban settlements; this knowledge is useful for the understanding of urban growth, to improve existing models of cities, in the context of sustainability, in studies about human mobility in urban areas, among other applications.