Diffusion-Limited Aggregation on Nonuniform Substrates

Diffusion-limited aggregation (DLA) on nonuniform substrates was investigated by computer simulations. The nonuniform substrates are represented by Leath percolations with the occupied probability p . p stands for the degree of nonuniformity and takes values in the range p c ≤ p ≤1, where p c is the threshold of percolation. The DLA cluster grows up on the Leath percolation substrate. The patterns of the DLA clusters appear asymmetrical and nonuniform, and the branches are relatively few for the case that p is close to p c . In addition, the pattern depends on the shape of substrate. As p increases from p c to 1, cluster changes to pure DLA gradually. Correspondingly, the fractal dimension increases from 1.46 to 1.68. Furthermore, the random walks on Leath percolations through the range p c ≤ p ≤1 were examined. Our simulations show the Honda–Toyoki–Matsushita relation is still reasonable for DLA growth in fractional dimensional spaces.