From the perspective of geography, urban territorial system and rural territorial system are two humanistic territorial systems coexisting on the earth’s surface. Due to the different roles played by urban territories and rural territories in the comprehensive surface process, including the evolution of the physical geography process and the human geography process, there are significant territorial functional differences (Fan,
2007;
2018). The transformation from a rural territorial function and system to an urban territorial function and system is called urbanization (Fan and Guo,
2019). Urbanization is the most important human geography process on the land surface, and it is also the basic trend of the evolution of regional development patterns (Chen
et al.,
2009). Urbanization not only leads to changes in territorial functional patterns but also to a gap in regional economic development (Wei,
1999). The study of changes in urban and rural distribution patterns and regional development patterns is an important proposition in geographic research, and the stable state and driving force of its distribution pattern evolution are the core scientific propositions of human geography (Fan
et al.,
2021). The basic principles of economic geography and the statistical laws of the development process of all countries worldwide show that the evolution process of regional development patterns can be expressed by the relationship between the regional development level and the regional economic gap. With the evolution of regional economic development levels, the development gap between regions shows an inverted U-shaped evolution law (Long,
1999). The maximum value of the gap, that is, the peak of the curve, generally appears when the per capita GDP reaches about 10,000 US dollars (Fan
et al.,
2019a). The regional gap changes from a low-level zero point to a high-level zero point through expanding and narrowing. In the process of evolution, whether it is the initial zero point or the final zero point, the narrowing and disappearance of the regional development gap is a manifestation of regional equilibrium. Regional development is a process that moves from a low-level equilibrium through disequilibrium to another high-level equilibrium. The key driving force is the potential energy formed by the development gap. The evolution law of the regional development gap is also applicable to the evolution of the urban and rural development gap. According to the classification of territorial function types, although urban territory and rural territory are two types of territorial units with different functions (Fan
et al.,
2006; Fan,
2007), the basic path to achieve coordination is consistent with regional equilibrium; that is, with economic development, the gap between urban and rural development continues to expand (Lu
et al.,
2019), and it begins to narrow after reaching its peak until coordinated development is achieved. Regional equilibrium processes and urban and rural equilibrium processes constitute an important theoretical basis for geographers to study regional pattern change (Fan and Zhao,
2021). In this study, the region is regarded as a complex with multiple function zones such as urbanization zones, food security zones, and ecological security zones. The regional gap is the gap between units with multiple functions, such as the gap between the east and west, the south and north. The direction of the urban and rural gap is relatively clear, referring to the differences between two different territorial types with clear functional directions. Functional difference and development gap constitute the two core aspects of regional disparity, the core proposition of geographical research. Therefore, studying the gap in regional development levels caused by functional differences between urban and rural territories is an important proposition in the study of regional differences in geography.