## 3 Results
### Distribution Results of Spatial Fractal Dimension in Xingdi Village  
The analysis of the fractal dimension of settlement subspaces requires the selection of 12 research samples. The selected study objects must meet two criteria: first, the settlement area should be sufficiently large to facilitate segmentation using appropriately sized grids; second, both the fractal dimensions of settlement buildings and suitable construction land should rank at a relatively high level within the sample. A higher fractal dimension value indicates greater overall spatial complexity of the village, making it more suitable as a subject for subsequent research. As indicated by the results in Section 3.1, Xingdi Village meets both conditions mentioned above. Its building fractal dimension is 1.650, which ranks above average within the sample, while its suitable construction area has a fractal dimension of 1.930, placing it at a high level. Additionally, this village covers a considerable area and is located at the foot of Mianshan Mountain, being recognized as the largest village in Mianshan Town. Within the settlement, there are distinct sections representing new and old villages, with new constructions situated to the south and older structures concentrated in central areas and along the western foothills. By employing a grid size of 150 m \(\times\) 150 m for subspace division, we delineated 67 regions within this settlement. The calculation and visualization results for each grid's fractal dimension are presented below (Figure 6). The calculation results indicate that the minimum fractal dimension of the settlement subspace is 1.326, while the maximum value reaches 1.763, with an average of 1.633. This demonstrates that the fractal dimensions of the settlement subspace are at a relatively high level. In terms of distribution, it can be observed that:  
Figure 6: Fractal dimension value. Overall, the subspace fractal dimensions of the settlement are predominantly concentrated in its central area, which serves as the core of the settlement. This region retains a diverse array of traditional architecture and fortifications while also representing a transitional zone between old and new structures within the settlement. As one moves toward the periphery of the settlement, there is a noticeable decrease in subspace fractal dimensions. The lowest fractal dimensions can be observed at both the easternmost and northernmost edges of the settlement. Analyzing topographical features reveals that to the southwest, there is a trend towards flatter terrain, whereas to the northeast, it gradually approaches the Mianshan Mountain range. Consequently, subspace fractal dimensions exhibit a radial decline towards this northeastern direction. 2. The settlement comprises two distinct parts: new villages and old villages. The boundary between these two areas is located along a main road situated to the south of the settlement, with old villages lying to its north and new villages to its south. Analysis indicates that on average, the subspace fractal dimensions in new village areas exceed those found in old village regions. 3. Focusing on specific notable zones within the settlement--such as well-preserved courtyards, fortress walls, and temples--reveals that these locations possess higher covering subregion fractal dimensions compared to their surrounding areas; for instance, regions like Huiluan Temple and East Fort exhibit significantly elevated fractal dimensions relative to nearby locales. 4. By overlaying these data with slope maps of the settlement's terrain (Figure 7), we can derive insights into potential correlations between fractal dimension values and topography. It becomes apparent that in areas characterized by relatively gentle slopes, subspace fractal dimensions tend to be larger; conversely, steeper terrains correspond with lower dimensional values. This observation suggests a possible relationship between topographic features and subspace fractal dimensions--a hypothesis warranting further investigation in subsequent studies.