Pattern of diffusion-limited aggregation on nonuniform substrate

Pattern of diffusion-limited aggregation (DLA) on nonuniform substrate was investigated by computer simulations. The nonuniform substrates are represented by Leath percolations with the probability p. p stands for the degree of nonuniformity and takes values in the range pc p 1, where pc 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 relative few for the case p is close to pc. In addition, the pattern depends on the shape of substrate. As p increases from pc to 1, cluster changes to pure DLA gradually. Correspondingly, the fractal dimension increases from 1.46 to 1.68. Also, the random walks on Leath percolations through the range pc p 1 were examined. Our simulations show the Honda–Toyoki–Matsushita relation is still reasonable for fractional dimensional systems.