三维分形聚集生长的计算机模拟

采用AGG模型(AggregationGenerationbyGenerationModel)在3种不同的近邻条件下和5种不同尺寸的网格中分别模拟了三维分形聚集体的生长过程,并计算了相应的逾渗阈值和分形维数。计算结果表明,分形聚集的逾渗阈值仅取决于空间维数和近邻条件,与模型的网格大小无关,是分形系统固有的临界属性。生长概率等于逾渗阈值时,聚集体可以无限生长并保持分形维数恒定;此时,分形维数只是空间维数的函数。

The computer simulation of three-dimensional fractal aggregation growth

We present AGG(Aggregation Generation by Generation)model to simulate the three- dimensional fractal aggregation process separately under three different neighbour conditions and five different lattice sizes,and calculate the percolation threshold values and the fractal dimensions correspondingly.The results suggest that the percolation threshold value of fractal aggregation is not related to the lattice size of the model,but only dependent on space dimension and neighbour condition,which is the inherent critical property of fractal system. The fractal aggregates can grow infinitely with the same fractal dimension when the growth probability is equal to the percolation threshold value.