  Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an
asymptotically safe theory which is applicable at arbitrarily small distance
scales. On sub-Planckian distances it predicts that spacetime is a fractal with
an effective dimensionality of 2. The original argument leading to this result
was based upon the anomalous dimension of Newton's constant. In the present
paper we demonstrate that also the spectral dimension equals 2 microscopically,
while it is equal to 4 on macroscopic scales. This result is an exact
consequence of asymptotic safety and does not rely on any truncation. Contact
is made with recent Monte Carlo simulations.
