Human mobility impacts many aspects of a city, from its spatial structure^1,2,3 to its response to an epidemic^4,5,6,7. It is also ultimately key to social interactions⁸, innovation^9,10 and productivity¹¹. However, our quantitative understanding of the aggregate movements of individuals remains incomplete. Existing models—such as the gravity law^12,13 or the radiation model¹⁴—concentrate on the purely spatial dependence of mobility flows and do not capture the varying frequencies of recurrent visits to the same locations. Here we reveal a simple and robust scaling law that captures the temporal and spatial spectrum of population movement on the basis of large-scale mobility data from diverse cities around the globe. According to this law, the number of visitors to any location decreases as the inverse square of the product of their visiting frequency and travel distance. We further show that the spatio-temporal flows to different locations give rise to prominent spatial clusters with an area distribution that follows Zipf’s law¹⁵. Finally, we build an individual mobility model based on exploration and preferential return to provide a mechanistic explanation for the discovered scaling law and the emerging spatial structure. Our findings corroborate long-standing conjectures in human geography (such as central place theory¹⁶ and Weber’s theory of emergent optimality¹⁰) and allow for predictions of recurrent flows, providing a basis for applications in urban planning, traffic engineering and the mitigation of epidemic diseases.

人口流动影响城市的许多方面，从其空间结构^1,2,3到其对流行病的反应^4,5,6,7。它也是社交互动⁸、创新^9,10和生产力¹¹的最终关键。然而，我们对个人总体运动的定量理解仍然不完整。现有模型——例如重力定律^12,13或辐射模型¹⁴——专注于流动性的纯粹空间依赖性，不捕捉重复访问同一地点的不同频率。在这里，我们揭示了一个简单而强大的比例定律，它根据来自全球不同城市的大规模移动数据来捕捉人口移动的时间和空间谱。根据该定律，任何地点的访问者数量随着访问频率和旅行距离的乘积的平方反比而减少。我们进一步表明，流向不同位置的时空流会产生突出的空间集群，其面积分布遵循 Zipf 定律¹⁵. 最后，我们建立了一个基于探索和优先回报的个体移动模型，为发现的尺度律和新兴的空间结构提供了机械解释。我们的研究结果证实了人文地理学中长期存在的猜想（例如中心位置理论¹⁶和韦伯的紧急最优性理论¹⁰），并允许预测循环流动，为城市规划、交通工程和流行病的缓解提供基础.