Tip-sticking probability and the branching distribution of a fractal pattern in a diffusion field

Abstract

We study the number of m-branch subsets M( m) on a two-dimensional off-lattice diffusion-limited aggregation simulation, where m is the number of particles of an m-branch. The M( m) decays exponentially, however, for small m its behavior is not simple. The probability distribution of each length subset P( m)= M( m)/ M all is independent of cluster size, where M all = ∑ m M(m) . The mean branch length L ̄ ≈2.34 is found from the above distribution. The P( m) is represented by a branching dynamic model (BDM) including only S tip≈0.785 which is the tip-sticking probability of a Brownian particle. Moreover, L ̄ ≈2.34 is related to S tip≈0.785. Therefore, we understand that the branching distribution is decided only by the tip-sticking probability.