Diffusion-limited aggregation on Sierpinski carpets is studied by computer simulation. We propose a fractal-cell generation method to form an infinite fractal lattice with the structure of Sierpinski carpets. The simulated results indicate that the exponent D, associated with the power-law behavior N∼${\mathit{R}}^{\mathit{D}}$, is dependent on the fractal dimension of Sierpinski carpet ${\mathit{d}}_{\mathit{f}}$.

• Received 11 July 1990

DOI:https://doi.org/10.1103/PhysRevA.43.4406