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Abstract 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. 

Information on urban built-up infrastructure is essential to understand the role of cities in shaping environmental, economic, and social outcomes. The lack of data on built-up heights over large areas has limited our ability to characterize urban infrastructure and its spatial variations across the world. Here, we developed a global atlas of urban built-up heights circa 2015 at 500-m resolution from the Sentinel-1 Ground Range Detected satellite data. Results show extreme gaps in per capita urban built-up infrastructure in the Global South compared with the global average, and even larger gaps compared with the average levels in the Global North. Per capita urban built-up infrastructures in some countries in the Global North are more than 30 times higher than those in the Global South. The results also show that the built-up infrastructure in 45 countries in the Global North combined, with ∼16% of the global population, is roughly equivalent to that of 114 countries in the Global South, with ∼74% of the global population. The inequality in urban built-up infrastructure, as measured by an inequality index, is large in most countries, but the largest in the Global South compared with the Global North. Our analysis reveals the scale of infrastructure demand in the Global South that is required in order to meet sustainable development goals.