Density pattern of functional facilities and its responses to urban development, especially in polycentric cities

With the increasing demand for facilities services, revealing the spatial pattern of various facilities with different functions (i.e., functional facility) and the driving role of urban attributes are crucial to improve the spatial equity of facilities, but still little is known. Here, we took 34 cities with different economic levels in China as cases. We assessed the density of nine types of functional facilities along the center-edge gradients, and analyzed the pattern disparity by cluster and correlation analyses. Results showed that facility density on the urban centeredge gradients presented a power-law attenuation, which was fitted for all types of functional facilities, even in the polycentric cities. The consistencies of attenuation rates increased with similarities of functional types of urban facilities, which reflects that the ability to provide facility services is closer. The attenuation rates decreased with the growth of the urban economy and built-up area, indicating the urban-rural dualization of facility distribution has slowed down accordingly. Furthermore, the relatively low attenuation rates of polycentric cities inspire the comprehensive planning based on facility pattern under the condition of limited urban land areas. This research supports improving the well-being of residents' access to various facility services, and further promotes the sustainable development of the cities.