Fractals from a reaction diffusion process

We introduce a reaction diffusion model on a lattice involving two particles species, A and B. B particles initially fill the lattice, and A particles diffuse transforming B particles to A particles each time they meet. We keep the number of A particles constant eliminating the oldest ones. The process builds empty clusters whose short time features are fractal (in the universality class of invasion percolation) and whose long-time features are those of compact objects.