Fractal Aggregation Near the Threshold

Abstract

In this papei, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is P" = 0.69It 0.02 for model 1 and P" -0.72 ± 0.01 for model 2, critical fractal dimension D c = 1.71 ± 0.06 for model 1 and D c = 1.66 ± 0.07 for model 2, which are in good agreement with those of DLA model (D = 5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be independent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class.