Traffic congestion is a major problem in megacities which increases vehicle emissions and degrades ambient air quality. Various models have been developed to address the universal features of traffic jams. These models range from microscopic car-following models to macroscopic collective dynamic models. Here, we study the macrostructure of congested traffic influenced by the complex geometry of the commute. Our main focus is on the dynamics of traffic patterns in Paris and Los Angeles, each with distinct urban structures. We analyze the complexity of the giant traffic clusters based on a percolation framework during rush hours in the mornings, evenings, and holidays. We uncover that the universality described by several critical exponents of traffic patterns is highly correlated with the geometry of commute and the underlying urban structure. Our findings might have broad implications for developing a greener, healthier, and more sustainable future city.