## 4 Discussion  
Discussion on the Fractal Dimension of Settlements and the Fractal Dimension of Suitable Construction Areas  
In the study of settlement morphology, researchers primarily focus on utilizing fractal dimensions for comprehensive analysis of settlements. Fractal dimensions reflect the intrinsic spatial order of complex systems and reflect self-similarity at both macro and micro levels [36]. The objects of fractal dimension analysis extend beyond merely the planar distribution patterns of settlement buildings; previous studies have also investigated building facades and street frontages within settlements to analyze their aesthetic forms [13; 37]. For mountainous settlements, construction is significantly influenced by topography, resulting in limited suitable areas for development that are often not contiguous. Consequently, village morphology tends to exhibit a dispersed point-like distribution [38; 39]. Suitable construction areas can effectively reflect the characteristics of the terrain and landforms. Based on the above points, we selected suitable construction areas as one of the subjects for fractal dimension analysis and sought to establish its correlation with the fractal dimensions of settlements. The fractal dimension of settlement building distribution reflects the spatial filling degree and complexity of settlements. The fractal dimension suitable for construction areas indicates the richness of land resource forms in mountainous settlements. Research has shown that traditional mountain settlements within the jurisdiction of Jiexiu City exhibit high spatial complexity. Villages with higher fractal dimensions, such as Zhang Village and Hongshan Village, have fractal dimensions of 1.72 and 1.71, respectively. These villages share certain common characteristics in their settlement morphology; both Zhang Village and Hongshan Village feature relatively organized new village areas that develop around ancient village regions, occupying a significant proportion of space. The well-planned new village areas demonstrate higher utilization rates due to their relative completeness in planning, which translates into greater spatial filling degrees and complexities. This significantly impacts the overall fractal dimension. Furthermore, constructing new villages around core ancient villages also influences the fractal dimension; this approach is more effective than rebuilding new villages in other areas, as it better complements settlement boundaries and enhances the spatial integrity of ancient villages. In our study, we found that while there are substantial proportions of new village areas adjacent to ancient villages--such as Jiaojia Fortress Village--their fractal dimensions do not reach similarly high levels. In terms of the fractal dimensions of suitable construction areas, all surveyed villages exhibited remarkably high fractal dimension values. This is primarily because the morphology of suitable construction areas in mountainous settlements is constrained and shaped by natural systems, which are inherently regarded as exemplary fractal systems [40]. Furthermore, a strong linear positive correlation was observed between the planar complexity of the twelve samples and the complexity of suitable construction areas. This suggests an intrinsic relationship between the planar morphology of settlement buildings and topographical features. In other words, the complexity of the terrain may significantly influence the spatial layout of settlement buildings, and the morphological characteristics of settlements, to some extent, reflect the complexity of their geographical environment. This finding further supports the hypothesis of a correlation between topography and the spatial morphology of settlements, laying a solid foundation for exploring the interaction mechanisms between settlements and their natural environment.