Characterizing the livingness of geographic space across scales using global nighttime light data

• A novel method for recursively extracting substructures from global nighttime images. • All substructures of global nighttime light image follow Zipf’s law. • The degree of liveliness as an indicator for characterizing global population distribution. The hierarchical structure of geographic or urban space can be well-characterized by the concept of living structure, a term coined by Christopher Alexander. All spaces, regardless of their size, possess certain degrees of livingness that can be mathematically quantified. While previous studies have successfully quantified the livingness of small spaces such as images or artworks, the livingness of geographic space has not yet been characterized in a recursive manner. Zipf’s law has been observed in urban systems and intra-urban structures. However, whether Zipf’s law is applicable to the hierarchical substructures of geographic space has rarely been investigated. In this study, we recursively extract the substructures of geographic space using global nighttime light imagery. We quantify the livingness of global cities considering the number of substructures (S) and their inherent hierarchy (H). We further investigate the scaling properties of the extracted substructures across scales and the relationships between livingness and population for global cities. The results demonstrate that all substructures of global cities form a living structure that conforms to Zipf’s law. The degree of livingness better captures population distribution than nighttime light intensity values for the global cities. This study contributes in three aspects: First, it considers global cities as a whole to quantify spatial livingness. Second, it applies the concept of livingness to cities to better capture the spatial structure of the population using nighttime light data. Third, it introduces a novel method to recursively extract substructures from nighttime images, offering a valuable tool to investigate urban structures across multiple spatial scales.