Diffusion-limited aggregation on nonuniform substrates

Diffusion-limited aggregation (DLA) on nonuniform substrates was investigat ed by computer simulations. The nonuniform substrates are represented by Le ath percolations with the occupied probability p. p stands for the degree o f nonuniformity and takes values in the range p(c) less than or equal to p less than or equal to 1, where p(c) is the threshold of percolation. The DL A cluster grows up on the Leath percolation substrate. The patterns of the DLA clusters appear asymmetrical and nonuniform, and the branches are relat ively few for the case that p is close to p(c). In addition, the pattern de pends on the shape of substrate. As p increases from p(c) to 1, cluster cha nges to pure DLA gradually. Correspondingly, the fractal dimension increase s from 1.46 to 1.68. Furthermore, the random walks on Leath percolations th rough the range p(c) less than or equal to p less than or equal to 1 were e xamined. Our simulations show the Honda-Toyoki-Matsushita relation is still reasonable for DLA growth in fractional dimensional spaces.