  We report on Monte Carlo studies of the critical behaviour of superfluid
$^4$He in the presence of quenched disorder with long-range fractal
correlations. According to the heuristic argument by Harris, uncorrelated
disorder is irrelevant when the specific heat critical exponent $\alpha$ is
negative, which is the case for the pure $^4$He. However, experiments on helium
in aerogel
  have shown that the superfluid density critical exponent $\zeta$ changes. We
hypothesize that this is a cross-over effect due to the fractal nature of
aerogel. Modelling the aerogel as an incipient percolating cluster in 3D and
weakening the bonds at the fractal sites, we perform XY-model simulations,
which demonstrate an increase in $\zeta$ from $0.67 \pm 0.005 $
  for the pure case to an apparent value of $0.722\pm 0.005$ in the presence of
the fractal disorder, provided that the helium correlation length does not
exceed the fractal correlation length.
