The Percolation Properties Of Fractal Aggregation

Firstly, We generalize the development of fractal theory, the definition of fractals and fractional dimension, and the physical mechanism of the fractal occurrence. Then, the diffusion limited aggregation (DLA), the ballistic aggregation (BA) and the reaction limited aggregation (RLA) models are introduced simply.And then, under different probabilities of growth and neighbor conditions, the modified model of random successive nucleation growth (RSNG) is adopted to simulate the one-dimensional growth of fractal aggregation, the aggregation generation by generation (AGG) model is used for two-dimensional growth, and the property of the critical percolation is studied emphatically. Main conclusions are summarized as follow.At the same the probability of growth (P), aggregate can grows more and more easily with loosening the neighbor condition. On the other hand, aggregate can also grows more and more easily with P increasing, under the same neighbor condition. So, the growth of aggregate is greatly affected by the probability of growth and the neighbor condition.The fractal aggregate begins to grow infinitely with the same fractional dimension when the probability of growth (P) is equal to the percolation threshold value (Pp). Under nearest, nearer, and third neighbor condition, the percolation threshold values are 0.800, 0.515 and 0.385 for one-dimensional growth, while 0.525, 0.265 and 0.165 for two-dimensional growth, respectively.The percolation threshold value (Pp) is not related to the size of model lattice but to near neighbor conditions. However, the fractal dimension of aggregate (D) is definite and independent of neighbor conditions, as P is equal to Pp.When P is equal to the critical threshold value Pc, aggregate begins to grow infinitely uniformly and does not keep its fractal structure. Under nearest, nearer, and third neighbor condition, the values of Pc are 0.83, 0.53 and 0.41 for one-dimensional growth, while 0.70, 0.34 and 0.25 for two-dimensional growth, respectively.Finally, the conclusion of this paper and the suggestion of further study are given.