Urban development is shaped by historical, geographical, and economic factors, presenting challenges for planners in understanding urban form. This study models commute flows across multiple U.S. cities, uncovering consistent patterns in urban population distributions and commuting behaviors. By embedding urban locations to reflect mobility networks, we observe that population distributions across redefined urban spaces tend to approximate log-normal distributions, in contrast to the often irregular distributions found in geographical space. This divergence suggests that natural and historical constraints shape spatial population patterns, while, under ideal conditions, urban organization may naturally align with log-normal distribution. A theoretical model using preferential attachment and random walks supports the emergence of this distribution in urban settings. These findings reveal a fundamental organizing principle in urban systems that, while not always visible geographically, consistently governs population flows and distributions. This insight into the underlying urban structure can inform planners seeking to design efficient, resilient cities.

翻译：城市发展受历史、地理和经济因素影响，这为规划者理解城市形态带来了挑战。本研究通过对美国多个城市的通勤流进行建模，揭示了城市人口分布和通勤行为中存在的稳定模式。通过嵌入反映流动网络的城市区位，我们观察到在重新定义的城市空间中，人口分布倾向于接近对数正态分布，这与地理空间中常见的不规则分布形成对比。这种差异表明，自然和历史约束塑造了空间人口格局，而在理想条件下，城市组织可能自然地趋向于对数正态分布。一个基于优先连接和随机游走的理论模型支持了该分布在城市环境中的涌现。这些发现揭示了城市系统中一个基本的组织原则：尽管地理上未必可见，但它持续支配着人口流动与分布。对城市底层结构的这一认识可为规划者设计高效、韧性的城市提供参考。