Unveiling intra-urban complexity and identifying urban cores through the lens of living structure using point-of-interest data

The intra-urban space is essentially an organized structure of complexity that consists of centers at different hierarchical levels or scales. This kind of complexity can be measured from the perspective of living structure inspired by Christopher Alexander’s organic view of space. Previous studies have revealed that the living structure can be used to characterize the structural complexity of photos, satellite images and urban systems. However, its potential to measure intra-urban complexity using massive point-based datasets remains underexplored. This study introduces a recursive method to analyze intra-urban complexity using massive point-of-interest (POI) data. By recursively decomposing urban substructures, we quantified structural complexity based on the livingness of substructures using a unified criterion. Our findings indicate that cities or intra-urban areas with higher livingness exhibit greater structural complexity. The resulting substructures exhibit power-law distributions and align closely with human activity patterns across multiple spatial scales in four large cities in China. Remarkably, intra-urban structures can be effectively understood with no more than four levels of recursive decomposition. Furthermore, we found that the urban centers or core areas can be effectively located using the proposed method. These insights underscore the potential of living structure as a framework for understanding and measuring the organized complexity of intra-urban spaces.