The attraction gradient of urban functions: How does functional mix at multiple scales predict urban vitality

What determines urban vitality has been a key research topic for urban planning and management since Jane Jacobs. Recently, statistical examinations of the relationship between the urban environment and vitality have become possible, facilitated by the availability of human positioning big data and fine-grained built environment data. However, existing studies tend to oversimplify the spatial impact of urban environmental factors, focusing solely on immediate surroundings. Due to people's trip chaining and exploration behavior, a place's functions can have a “spill-over” effect across the urban space. This study, therefore, aims to investigate such “attraction gradient” of urban functions to better understand the spatial relationship between urban vitality and its influencing factors. The study uses mobile phone and point-of-interest data from Beijing and Chengdu, China, to model the relationship between a place's vitality and urban functions in different distance bands. We find that, when counting from a place, urban functions within five kilometers significantly predict urban vitality, whereas beyond five kilometers, their contribution is marginal. Daytime and nighttime attraction gradients also differ. This study offers insights into the spatial relationship between urban function and vitality, enhancing our understanding and modelling of urban vitality.