## 4 Spatiotemporal Evolution Characteristics  
### Generally Stable Spatial Development Trend  
The application of the standard deviation ellipse calculation method provided insightful revelations into the spatial dynamics of Paomo restaurants within Xi'an's central urban area. This methodological approach highlighted a pronounced trend of outward spatial expansion in these establishments. Despite a varied rate of development across different sectors of the area, the overall growth pattern maintained a level of stability, as illustrated in Figure 5. The analysis indicated that the area encompassed by the ellipse in 2012 was considerably more compact, demonstrating a higher degree of aggregation. However, by 2023, the ellipse had expanded by 32.21%, signifying a significant outward shift in both population and land use within the central urban area. This expansion substantially exceeded the rate of construction land growth, which was about 20% over the same period, thereby underscoring a dynamic and vigorous development in the local catering sector.  
Additionally, the coordinates of the ellipse's center revealed subtle shifts in the spatial distribution center of Paomo restaurants during the research period. These establishments remained predominantly clustered around Xi'an's historic city wall, with only a minor northward movement of approximately 287 m, as detailed in Table 1. The area of the ellipse increased from 312.43 km\({}^{2}\) in 2012 to 413.03 km\({}^{2}\) in 2023, showing a substantial growth of 100.6 km\({}^{2}\), or approximately 32.2%. This expansion indicates a notable outward spread of Paomo restaurants, suggesting a growing influence of this culinary type in the urban landscape. The slight shifts in the X and Y center points (from 108.9343\({}^{\circ}\) to 108.93615\({}^{\circ}\) and from 34.248831\({}^{\circ}\) to 34.251326\({}^{\circ}\), respectively) represent a minor northward movement. This northward shift of roughly 287 m suggests a gradual relocation of the density center of Paomo restaurants within the city, potentially reflecting new urban developments or shifts in the population center. The lengths of both the X-axis and Y-axis increased over the period, with the X-axis growing by 139.25 m and the Y-axis by 159.19 m. These changes underscore an increase in the spatial footprint of Paomo restaurants, both in width and depth, indicative of a robust expansion in their geographic distribution. The rotation angle of the ellipse increased from 67.34\({}^{\circ}\) in 2012 to 77.22\({}^{\circ}\) in 2023, adjusting by 9.88\({}^{\circ}\). This rotation suggests a change in the orientation of the spatial distribution, possibly aligning more closely with changes in urban infrastructure such as road development or shifts in commercial and residential layouts. The observed changes in the spatial characteristics of the Paomo restaurants not only reflect the industry's growth but also have implications for urban planning and development. The increased area and altered orientation could influence urban transportation planning, zoning decisions, and resource allocation to better accommodate and leverage the growth of the Paomo restaurant industry. Overall, this analysis reveals that the Paomo restaurants are not only increasing their reach  
Figure 5: POI Standard Deviation Ellipse Analysis for Xi’an City Center Paomo Restaurants.  
within Xi'an's central urban area but also possibly adapting to or influencing new urban development patterns. This evolution in spatial distribution might also reflect broader socio-economic trends, such as shifts in consumer behavior, population movement, and urban expansion policies.