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While the daily ebb and flow of people across a city might seem chaotic, new research reveals underlying universal patterns. A study published in the leading international journal Nature Communications by a team led by Chair Professor Bo Huang from the Department of Geography at the University of Hong Kong (HKU) unveils fundamental spatiotemporal scaling laws that govern these population dynamics.

Understanding how people move and distribute themselves within cities is crucial for effective urban planning and management. While technology has provided vast amounts of data on where people go, grasping the temporal rhythms of population density across different locations has remained a challenge. Professor Huang's team tackled this gap by applying complexity science principles to analyse large-scale mobile device data from major cities worldwide.

"We found that seemingly random population movements are governed by organised principles," explains Professor Huang, the corresponding author. "These principles connect the temporal pulse of the city to its physical structure, showing that population dynamics scale predictably with urban density and distance from central hubs." Their findings, detailed in the article "The spatiotemporal scaling laws of urban population dynamics", demonstrate that:

1. Predictable Patterns Emerge: Contrary to appearances, daily population fluctuations are not random. They follow predictable "scaling laws" – mathematical relationships that hold true across different time intervals and geographical scales within a city.
2. City-Wide Consistency: At the scale of the entire city, these fluctuations exhibit consistent spatiotemporal patterns, describable by power-law functions.
3. Local Dynamics and Distance Decay: At specific locations (micro-level), fluctuations also follow scaling laws over time. Crucially, the intensity of these dynamics diminishes with increasing distance from urban centers, similar to how indicators like population density decrease. This decay follows an "allometric model," connecting the vibrancy of population dynamics to the density of urban features, such as points of interest (POIs).
4. Linking Space and Time: The research establishes a novel logarithmic relationship between the spatial decay and the temporal scaling, effectively linking how population dynamics change over time and across urban space.

This study offers significant theoretical advances by extending scaling concepts in urban science firmly into the temporal domain, forging a new link between space and time dynamics, and offering fresh perspectives on how cities self-organise. Practically, the research enables the creation of "space-time spectra" maps (Figs. 1 & 2) that visualise population dynamics across a city. This provides a powerful, activity-based view of the city's functional structure.

"This deeper understanding has direct implications," says Dr Xingye Tan, a postdoctoral researcher and co-first author with Professor Huang. "It can inform more effective urban planning, optimise commercial and transportation strategies, guide infrastructure development, and aid in managing public health challenges, ultimately helping build more livable, resilient, and sustainable cities."

The collaborative research team includes Professor Michael Batty (University College London), Assistant Professor Weiyu Li (Suzhou University of Science and Technology), Associate Professor Qi Wang (Northeastern University, USA), Assistant Professor Yulun Zhou (Department of Urban Planning and Design, HKU), and Professor Peng Gong, Vice-President (Academic Development) and Chair Professor in the Department of Geography at HKU.

The full paper can be accessed at: https://www.nature.com/articles/s41467-025-58286-4.

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