Understanding the spatial structure and evolution of Kaifeng based on entropy and fractal analysis

Given China’s rapid urbanization in the 21st century, understanding the complexity of its spatial structure is crucial for appropriately regulating the country’s urban development. Entropy and fractal analysis are two important quantitative means for describing the complexity of geographical space. These two methods can be integrated to comprehensively analyze the characteristics of self-organization and evolution of the urban spatial structure, as well as the internal factors driving this process. As a typical single-center city in the Central Plain of the country, Kaifeng City is representative of the rapid urbanization of China in the past four decades. This study uses data on Kaifeng City from 1980 to 2020 to examine the spatial entropy of the structure and evolution of its built-up land, and to subject it to a multi-fractal analysis. The results show that the spatial entropy of built-up land in Kaifeng City has been increasing in the last four decades, and the degree to which its urban space is filling up has been increasing each year. The spatial entropy of the urban center is higher than that of the surrounding areas, while built-up areas in the region have become more orderly. The multi-fractal analysis further reveals that Kaifeng City has undergone prominent spatial expansion, and its built-up land has expanded particularly rapidly in the past two decades. Changes in the central and marginal areas of the city have been asynchronous and periodic, where the marginal areas have undergone a disorderly expansion. The heterogeneity of urban space has gradually decreased. The work here provides a comprehensive understanding of the patterns of urban spatial expansion as well as the structure of land use.