Formations of fractal islands aggregated with discs in Gaussian distribution on nonlattice substrates

The growth mechanism of fractal islands on a two-dimensional nonlattice sub strate with periodic boundary conditions has been investigated by using Mon te Carlo technique. Results show that the fractal dimension di of the final ramified islands is almost independent of the diffusion step length, mobil ity and rigid rotation of the islands. The characteristics of the size dist ribution of the discs in an island do not change the dimension d(f) of the island. However, we find that df increases linearly with the surface covera ge rho of the system and its slope decreases with the increase of the mean diameter of the discs.