## 2 Materials and Methods
### Methods
#### 2.3.3 Dynamic Iteration Module  
The execution order of the dynamic iteration module is determined by the unallocated quantity of various types of land, and the land types with large demand for land expansion are given priority. Before the iteration starts, the overall conversion probability of each type of land is sorted according to the size of the value, and the corresponding cell position (i.e., high-quality seed points) is recorded. Each land use type selects the location of the expansion from large to small according to the overall conversion probability during the iteration, and then performs the following seed planting. Seed planting involves multi-purpose land competition, and the basis for winning is the overall conversion probability. The specific process of the dynamic iteration process is shown in Figure 8.  
Figure 7: Neighborhood probability of conversion to six types of land from 2015 to 2020.  
In Figure 8, \(OP_{i,k}\) denotes the overall transition probability of k on cell \(i\). Cell \(i\) is the selected high-quality seed points. The formula is:  
\[OP_{i,k}^{t}=P_{i,k}\times C_{i,k}^{t}\times R \tag{8}\]  
where \(k\) represents the state of the cell \(i\). \(P_{i,k}\) represents the LUCC suitability at cell \(i\). \(C_{i,k}^{t}\) is the constraint condition, which limits the expansion of some land types according to local policies or the mutual conversion of historical land types. The expression formula of \(C_{i,k}^{t}\) is:  
\[C_{i,k}^{t}=con(S_{i}^{t-1}=Landuse_{k}) \tag{9}\]  
where \(S_{i}^{t-1}\) represents the state of the cell \(i\) in iteration \(t-1\) times. When \(S_{i}^{t-1}\) is a restricted land type, the value of \(con()\) is 1. Otherwise, the value of \(con()\) is 0. In this paper, the impermeable layer cannot be converted to other land use/cover types because of the high cost of converting the impermeable layer to other types of land.  
According to the study of [PERSON] et al. [27], the random disturbance factor \(R\) is introduced to make the simulation results more in line with the period. The expression formula of \(R\) is:  
\[R=1+(-\ln\gamma)^{\alpha} \tag{10}\]  
where \(\gamma\) is a uniform random variable in the interval from 0 to 1. \(\alpha\) is the parameter to control the size of random disturbance, which is 5 in this paper.  
\(TM_{i,k}\) is a transformation matrix that defines whether the original type of cell \(i\) is allowed to be converted to type k. Considering the changes between different land types every 5 years from 2000 to 2020, the value corresponding to the two land types that have not been converted is 0, indicating that conversion is not allowed. The rest are 1, indicating that conversion is allowed.  
The \(MOP_{i}^{t}\) represents the maximum comprehensive conversion probability of the cell \(i\) at the current time, and its value is dynamically updated with the increase in the number of iterations of the CA model. By comparing the comprehensive conversion probability of the cell \(i\) converted to different land types, the competition of multiple land types is realized.  
Figure 8: Flowchart of CA model based on high-quality seed selection iterative algorithm (HQSSIA).