The spatiotemporal scaling laws of urban population dynamics.

Human mobility is becoming increasingly complex in urban environments. However, our fundamental understanding of urban population dynamics, particularly the pulsating fluctuations occurring across different locations and timescales, remains limited. Here, we use mobile device data from large cities and regions worldwide combined with a detrended fractal analysis to uncover a universal spatiotemporal scaling law that governs urban population fluctuations. This law reveals the scale invariance of these fluctuations, spanning from city centers to peripheries over both time and space. Moreover, we show that at any given location, fluctuations obey a time-based scaling law characterized by a spatially decaying exponent, which quantifies their relationship with urban structure. These interconnected discoveries culminate in a robust allometric equation that links population dynamics with urban densities, providing a powerful framework for predicting and managing the complexities of urban human activities. Collectively, this study paves the way for more effective urban planning, transportation strategies, and policies grounded in population dynamics, thereby fostering the development of resilient and sustainable cities.