# Dynamic Mechanism of Dendrite Formation in Zhoukoudian, China
## 4 Result and Discussion  
Figure 3 shows the computer simulation results of the DLA model, with L = 200 lattice and 20,000 particles. Figure 3a,b shows the simulated growth results when 8057 and 10,827 random particles are released, respectively, and Figure 3c shows the dendritic graph obtained after running the program (20,000 particles). From Figure 3, it can be clearly seen that the tree branches simulated by the DLA model continue to grow upward. It seems that the larger DLA cluster has more arms and fills the space more evenly than does the smaller cluster; its fractal dimension is 1.59 (Figure 4). Figure 5 shows the computer simulation results of the DLA model, with lattice L = 250 and 30,000 random particles. This dendritic fractal pattern is relatively complex. Particles grow outward from the central seed. The dendritic pattern formed is gradually complicated. The fractal dimensions of the dendritic pattern shown in Figures 3 and 5 were calculated, using the box dimension method, to be 1.59 and 1  
extraction analysis location \(\rightarrow\) image processing \(\rightarrow\) image binary matrix data extraction \(\rightarrow\) data statistical analysis, the box dimension method was used to calculate the morphological fractal dimension of the four samples in Zhoukoudian area. The results show that the fractal dimension of the four samples is 1.61, 1.67, 1.78, and 1.52, respectively, ranging from 1.52 to 1.78, with an average value of 1.65. The local fractal dimension of JZG03 is 1.77, while the overall fractal dimension is 1.78, indicating that the local pattern of the dendrite shows self-similarity to the overall pattern; that is, the dendritic pattern of dendrite has fractal characteristics. The fractal dimensions of the dendritic pattern simulated by the DLA model are 1.59 and 1.64, which are consistent with the fractal dimensions of Zhoukoudian dendrite. The simulation effect is good, which essentially reveals the microscopic dynamic mechanism of dendrite formation. Figure 4: Fractal dimension of dendritic pattern simulated by 20,000 particles (as shown in Figure 3). Figure 5: Dendritic pattern simulated by DLA (250 \(\times\) 250 lattice, 30,000 particles). From the above, the agglomeration group (cluster) formed by the DLA model exhibits fractal characteristics. Moreover, previous studies have shown that the fractal dimension of DLA is independent of the lattice type [20]. The fractal dimension of the obtained DLA figure remains unchanged when the square lattice is changed into a triangular lattice [20], its fractal dimension does not increase with the increase in the spatial dimension, and it has a stable value [25]. DLA also has a screening effect [20]. The reason for the generation of branches with different sizes is that, due to the tortuous random motion trajectory of the particles, the branches that extend from the outside of the cluster have a greater probability of acquiring particles, which prevents the particles from intruding into the inside. This screening effect makes the clusters grow in the structure by continuously branching outward [26]. Figures 3 and 5 also show that, in the process of the random walking and outward growth of the particles, due to the high probability of obtaining particles from the branches extending outside the cluster, particles cannot invade into the interior. This screening effect makes the cluster grow continuously according to the outward branching structure, forming a complex dendritic pattern. According to the above analysis, it is believed that the formation of dendrite is a fractal pattern formed in the process of fractal growth, that is, the microscopic dynamic mechanism of its formation. In recent years, studies regarding fractal growth have developed rapidly [27; 28; 29; 30; 31]. According to the latest research results, fractal growth phenomena caused by self-organized criticality can be generally summarized into three main models: Laplace, percolation, and oscillation.