  We compute the intrinsic Hausdorff dimension of spacetime at the infrared
fixed point of the quantum conformal factor in 4D gravity. The fractal
dimension is defined by the appropriate covariant diffusion equation in four
dimensions and is determined by the coefficient of the Gauss-Bonnet term in the
trace anomaly to be generally greater than 4. In addition to being testable in
simplicial simulations, this scaling behavior suggests a physical mechanism for
the screening of the effective cosmological `constant' and inverse Newtonian
coupling at very large distance scales, which has implications for the dark
matter content and large scale structure of the universe.
