## 3 Results  
### Calculation Results of Fractal Dimension for Urban Settlements  
Through the preprocessing of data, we conducted a fractal dimension calculation on the building distribution maps and suitable construction area distributions of 12 research samples. The results are presented in Table 2.  
Through calculations, the average fractal dimension of settlement buildings reached 1.624, while the average fractal dimension of suitable construction areas was 1.868. Both values are considered relatively high within the jurisdiction of Jiexiu City. Generally, the fractal dimension of settlement buildings is lower than that of suitable construction areas. Among them, Banyu Village has a smaller settlement with a dispersed building distribution; its fractal dimensions for both settlements and suitable construction areas are the lowest recorded, with a minimal difference of only 0.220. In contrast, Zhangcun Village features a larger settlement characterized by dense building arrangements and higher building volume ratios; it exhibits the highest fractal dimensions for both categories, 1.720. The smallest difference between these two indices is found in Hongshan Village, which shows a discrepancy of merely 0.190, whereas Dajin Village displays the largest gap at 0.290. Using SPSS to conduct correlation analysis on the fractal dimensions of the study sample buildings and those in suitable construction areas yielded the results shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Village**} & **Architectural** & **Suitable Construction Area** & **Difference** \\  & **Fractal Dimension** & **Fractal Dimension** & **Difference** \\ \hline Dajin & 1.630 & 1.920 & 0.290 \\ Xingdi & 1.650 & 1.930 & 0.280 \\ Nanzhuang & 1.583 & 1.860 & 0.277 \\ Jiaojialbao & 1.585 & 1.850 & 0.265 \\ Xiaojin & 1.620 & 1.880 & 0.260 \\ Zhangbi & 1.660 & 1.918 & 0.258 \\ Xialihou & 1.690 & 1.930 & 0.240 \\ Zhang & 1.720 & 1.950 & 0.230 \\ Banyu & 1.470 & 1.690 & 0.220 \\ Tian & 1.584 & 1.880 & 0.216 \\ Liujiashan & 1.590 & 1.790 & 0.200 \\ Hongshan & 1.710 & 1.900 & 0.190 \\ \hline \end{tabular}
\end{table}
Table 2: Fractal dimension results of urban settlements.  
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{
\begin{tabular}{c} **Architectural Fractal** \\ **Dimension** \\ \end{tabular} } & **Suitable Construction** \\  & **Dimension** & **Area Fractal Dimension** \\ \hline Architectural fractal & 1 (0.000 ***) & 0.841 (0.001 ***) \\ dimension & 0.841 (0.001 ***) & 1 (0.000 ***) \\ \hline \end{tabular}
\end{table}
Table 3: SPSS regression results.  
The analysis results indicate a strong positive correlation between the two variables, with a correlation coefficient reaching as high as 0.841, which is statistically significant (\(p<0.001\)). This suggests that as the fractal dimension of settlement architecture increases, the fractal dimension of suitable construction areas also rises concurrently. This preliminary finding reveals the intrinsic relationship between topography and the spatial morphology of settlement architecture, providing data support and a research foundation for further exploration of the interaction mechanisms between the two.