Formation of fractal islands on nonlattice substrates

Abstract

A Monte Carlo study on the formation of fractal islands on nonlattice substrates is presented. The islands, including disc aggregates and single discs, perform two-dimensional diffusion along four directions with different diffusion step lengths and rigid rotation about their centers of mass on a nonlattice square with periodic boundary conditions. It is found that the fractal dimension of the ramified islands is almost independent of the diffusion step length, rigid rotation angle, and disc size. However, the fractal dimension increases linearly with the surface coverage. Our simulation results are in good agreement with the previous experimental findings of the aggregation of the silver atomic islands on silicone oil surfaces.