Characteristics of Coupling between Multi-scale Community Living Circles Public Service Facilities Supply and Spatial Centers

In response to changing demand structures due to slower population growth and economic shifts, this study examines the coordination between public service facilities and urban spatial centers, crucial for people-centered community development and spatial agglomeration laws. Utilizing crystal-growth algorithms and spatial autocorrelation, the research algorithmically interprets spatial centers, and conducts kernel density and natural break classification analyses on public service facilities. The case of Guangzhou's central urban area reveals: 1) The spatial centers are in Liwan, Yuexiu, and Haizhu districts; 2) Centers are dispersed within a five-minute range but cluster over thirty minutes; 3) Analysis of coupling at different scales highlights areas needing more public service facilities. This methodology elucidates the relationship between spatial elements and structure, enriching community living circle theory and contributing to urban high-quality development.