计算模拟8-fractal.ppt

FUNCTION PARTICLE_MERGE( ) INTEGER :: PARTICLE_MERGE PARTICLE_MERGE=1 IF(Site(p_x-1,p_y).eq.1) go to 10 IF(Site(p_x+1,p_y).eq.1) go to 10 IF(Site(p_x,p_y-1).eq.1) go to 10 IF(Site(p_x,p_y+1).eq.1) go to 10 RETURN 10 cluster_num=cluster_num+1 cluster_x(cluster_num)=p_x cluster_y(cluster_num)=p_y Site(p_x,p_y)=1 x_x=SQRT(((p_x-X_0)**2+(p_y-Y_0)**2)*1.) IF(x_x.gt.r_max)then r_max=x_x r_delete=2*r_max END IF PARTICLE_MERGE=0 END FUNCTION PARTICLE_MERGE FRACTAL GROWTH PROCESSES FRACTAL GROWTH PROCESSES FRACTAL GROWTH PROCESSES Cluster-cluster aggregation: Fractal structures commonly occur in aggregates that have been formed by the clustering of particles that are diffusing in a fluid. FRACTAL GROWTH PROCESSES lattice with periodic boundary conditions. In a typical simulation we begin with a dilute collection of N particles. Each of these particles is a cluster with unit mass. The particles do random walks until one of them becomes a nearest neighbor of another particle. At that point they stick together to form a cluster of two particles. This new cluster now moves as a single random walker with reduced diffusion coefficient. As this process continues, the clusters become larger and fewer in number. For simplicity, we assume a square * * Many systems occurring in nature exhibit fractal geometry. coastlines, clouds, coral reefs, and the human lung… FRACTAL GROWTH PROCESSES coastlines clouds leaves coral reefs coral reefs human lungs Why are fractal structures so common? How do fractal structures form? We discuss several simple “growth” models that generate structures which show a remarkable similarity to forms observed in nature. FRACTAL GROWTH PROCESSES FRACTAL GROWTH PROCESSES where is the length of the small object, is the total number measured by the small object. Fractal dimension: (Hausdorff) FRACTAL GROWTH PROCESSES ? FRACTAL GROWTH PROCESSES Eden model It was proposed by Eden in 1958 to simulate the growth