This article analyzes the complex geometry of urban transportation networks as a gateway to understanding their encompassing urban systems. Using a proposed ring-buffer approach and applying it to 50 urban areas in the United States, we measure road lengths in concentric rings from carefully-selected urban centers and study how the trends evolve as we move away from these centers. Overall, we find that the complexity of urban transportation networks is naturally coupled, consisting of two distinct patterns: (1) a fractal component (i.e., power law) that represent a uniform grid, and (2) a second component that can be exponential, power law, or logarithmic that captures changes in road density. From this second component, we introduce two new indices, density index and decay index, which jointly capture essential characteristics of urban systems and therefore can help us gain new insights into how cities evolve.
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