  The scaling behavior of linear polymers in disordered media, modelled by
self-avoiding walks (SAWs) on the backbone of percolation clusters in two,
three and four dimensions is studied by numerical simulations. We apply the
pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results
yield estimates of critical exponents, governing the scaling laws of disorder
averages of the configurational properties of SAWs, and clearly indicate a
multifractal spectrum which emerges when two fractals meet each other.
