Table 1 The landscape metrics selected in this study

Number of patches (NP)

NP is the total number of patches

Total class area (CA)

\(CA=\sum_{i=1}^{n}{a}_{i}\), \({a}_{i}\) is the area of patch i

Mean patch size (MPS)

\(MPS=\sum_{i=1}^{n}{a}_{i}/n\) ai, \({a}_{i}\) is the area of patch i, n is the count of patches

Largest path index (LPI)

\(LPI=100{a}_{max}/A\), \({a}_{max}\) is the maximum patch area, A is the total patch area and is a simple dominance measurement algorithm

Mean shape index (MSI)

\(MSI=0.5P/\sqrt{\pi A}\), P is the total length of the patch boundary, while A is the total area of the patch. When comparing the shape to that of a circle, a value closer to 1 indicates a greater tendency towards a circular shape

Mean patch fractal dimension index (MPFD)

\(MPFD=\sum_{i=1}^{n}(\frac{2ln0.25{P}_{i}}{ln{a}_{i}})/n\), MPFD is the mean settlement fractal dimension, where \({P}_{i}\) is the perimeter of patch. \({a}_{i}\) is the area of patch i; n is the number of patches. The index serves to assess the complexity and variability of settlement patch boundaries, with larger values indicating a greater intricacy in the shape of the settlement