Examining the spatial configuration of street junctions across cities: a fractal approach on intra-urban clusters

• Propose an α–β framework for multi-scale comparison of urban form and function. • Derive α (form) and β (function) parameters from fractal-based scaling profiles. • Enable objective, cross-city comparison through quantifiable analysis of urban morphology. Urban streets form the backbone of cities, and variations in street-junction spatial configuration provide valuable insights into urban form and function, both of which exhibit fractal and scaling characteristics in their structural and statistical properties. However, these patterns emerge from the interaction of multiple spatial processes operating at different scales, making it difficult to capture and compare their form-function relationships using single-scale analyses. To address this challenge, this study proposes a new α–β framework for multi-scale urban form comparison, grounded in fractal theory. Using a progressive clustering method, we construct scaling profiles for multiple cities, deriving the α (form) and β (function) parameters to systematically compare urban structures with differing morphologies and to identify urban clusters at their characteristic scales. This approach transforms the subjective perception of morphology into an actionable analytical tool, enabling integrated form-function assessment and overcoming the challenges of comparative studies from different urban systems. Overall, the proposed α–β framework effectively deconstructs urban complexity, as evidenced by its application to a comparative analysis of nine global metropolises.