Research on fractal dimension and growth control of diffusion limited aggregation

Abstract

The fractal theory is a significant research subject in which diffusion limited aggregation (DLA) is a valuable model. DLA is a simple model which can reflect a wide range of natural phenomena. Through simple kinematic and dynamic processes, it can produce a self-similar fractal structure with scale invariance. The growth process is dynamic far from equilibrium, but the cluster structure has a stable and definite fractal dimension. In this paper, we study the fractal dimension of DLA, try to control the growth of DLA, and simulate the growth process that may occur in some natural environments under some factors. We use simple java code to build a DLA growth model. We use a fixed number of particles and the DLA of particle aggregation to touch the set boundary as the boundary conditions, respectively. We simulate the process of particle random motion aggregation into DLA clusters and generate images to observe the results. We use the density method to compute the fractal dimension of DLA. To control the growth of DLA, we modify some parameters of the random motion process of particles, including the step size, the probability of moving in different directions, the initial generation region of particles and so on. By analyzing the fractal dimension, we find that the fractal dimension of DLA can be greatly affected by changing the area of particles. In the study of the growth control of DLA, we mainly study the influence of changing the probability of particles moving in different directions on the growth of DLA (some specific factors can cause this effect in the natural environment). Through these changes, we can make DLA grow in a fixed direction. We can analyze the growth of fractal systems in the real situation through these straightforward simulations, which are computer programs based on DLA principles.