Percolation analysis of spatiotemporal distribution of population in Seoul and Helsinki.

Spatiotemporal distribution of urban population is crucial to understand the structure and dynamics of cities. Most studies, however, have focused on the microscopic structure of cities such as their few most crowded areas. In this work, we investigate the macroscopic structure of cities such as their clusters of highly populated areas. To do this, we analyze the spatial distribution of urban population and its intraday dynamics in Seoul and Helsinki with a percolation framework. We observe that the growth patterns of the largest clusters in the real and randomly shuffled population data are significantly different, and highly populated areas during the daytime are denser and form larger clusters than highly populated areas during the nighttime. An analysis of the cluster-size distributions at percolation criticality shows that their power-law exponents during the daytime are lower than those during the nighttime, indicating that the spatial distributions of urban population during daytime and nighttime fall into different universality classes. Finally measuring the area-perimeter fractal dimension of the collection of clusters demonstrates that the fractal dimensions during the daytime are higher than those during the nighttime, indicating that the perimeters of clusters during the daytime are rougher than those during the nighttime. Our findings suggest that even the same city can have qualitatively different spatial distributions of population over time, and propose a way to quantitatively compare the macrostructure of cities based on population distribution data.