Results of asymptotic safety related investigations indicate that the effective spacetimes of QEG have fractal -like properties on microscopic scales. It is possible to determine, for instance, their spectral dimension and argue that they undergo a dimensional reduction from 4 dimensions at macroscopic distances to 2 dimensions microscopically. In this context it might be possible to draw the connection to other approaches to quantum gravity, e.g. to causal dynamical triangulations, and compare the results.