[en] This paper studies the spatiotemporal evolution characteristics of traffic dynamics at a crossroads which consists of two perpendicular one-lane roads, employing alternating update rules and periodic boundary conditions. Unlike in previous studies, the deterministic Nagel–Schreckenberg traffic flow model is adopted in this work. Based on a close observation of the evolution near the upstream and downstream traffic flow at the crossing point, we have found typical periodically recurring sequences of vehicle motion configurations, and their specific characteristics depend on the value of the maximum velocity of vehicles and the vehicle densities on both roads. We have presented phase diagrams which consist of five basic regions. The flow formulas in these regions have been analyzed or derived. The results of theoretical analysis are in good agreement with the simulation results. (paper: interdisciplinary statistical mechanics)