THE CRITICAL-POINT OF FRACTAL PERCOLATION IN 3 AND MORE DIMENSIONS

The fractal percolation model is constructed by the progressive replacement of each cube by a random collection of sub-cubes, each sub-cube being retained with probability p. There is a critical probability p(c)(M, d) depending on the dimension d and the substitution ratio M. We point out that, for large M, the value of p(c)(M, d) is near to that of site percolation on a lattice derived from the d-dimensional hypercubic lattice by the addition of certain bonds.