A segmented fractal model for representing the spatial distribution features of urban road networks

In view of the limitations of fractal models with a single fractal dimension in characterizing the spatial distribution nonuniformity of road networks, this study summarizes the multiscale variation patterns of road networks' length in space and establishes a segmented fractal model that reflects the spatial distribution features of road networks. This model maintains the essential measurement foundations of fractal theory and enhances the ability to characterize spatial distribution nonuniformity by associating segmented model parameters with spatial distribution features. Using the road networks of developed cities as experimental subjects, this study further clarifies the underlying mechanisms of the parameters in the segmented fractal model. The results demonstrate that the segmented fractal model divides the road networks into two regions based on the segmented point. The fractal dimension derived for each region can characterize the heterogeneity of road networks' length growth. Moreover, the position of the segmented point exhibits significant positive correlations with the parameters of the spatial distribution analysis model, including standard distance, semi-major axis, and semi-minor axis, with corresponding correlation coefficients of 0.89, 0.92, and 0.85, respectively. These findings demonstrate that the segmented point carries valuable spatial information, serving as a quantitative reference for evaluating spatial distribution features and providing methodological support for urban transport network planning and optimization.