A study of open spaces of urban bays in Qingdao, China: from the perspective of fractal order

Urban bays in coastal cities like Qingdao play a pivotal role in fostering sustainable human-nature symbiosis amid rapid urbanization. However, economic-driven development has led to fragmented spatial hierarchies and heterogeneous open space distributions, limiting their capacity to meet diverse user demands. Despite their importance for localized human-environment interactions, small-scale bays have received limited scholarly attention. This study addresses this gap by employing fractal theory to analyze the hierarchical structure, scale transitions, and spatial organization of open spaces in two contrasting bays: Qingdao Bay (historically evolved) and Fushan Bay (modern development). Using grid fractal dimension analysis, box-counting methods, and GIS tools, we quantify fractal characteristics, identify scale discontinuities, and evaluate spatial balance. Results reveal that Qingdao Bay exhibits a fractal dimension of 1.784 (R² = 0.998), aligning closely with ideal urban fractal patterns, while Fushan Bay’s higher fractal dimension (1.839, R² = 0.999) indicates excessive spatial fragmentation. Key issues include oversized coastal parks disrupting scale continuity, insufficient human-scale interaction spaces, and homogeneous functional zoning. To address these, we propose a fractal-optimized hierarchical framework emphasizing multi-scale integration, transitional spaces, and mixed-use planning. This research advances the application of fractal theory to small-scale coastal systems in Qingdao, offering actionable insights for enhancing spatial quality within similar urban bay contexts.