  We perform a first investigation of the coupling constant flow of the
nonperturbative lattice model of four-dimensional quantum gravity given in
terms of Causal Dynamical Triangulations (CDT). After explaining how standard
concepts of lattice field theory can be adapted to the case of this
background-independent theory, we define a notion of "lines of constant
physics" in coupling constant space in terms of certain semiclassical
properties of the dynamically generated quantum universe. Determining flow
lines with the help of Monte Carlo simulations, we find that the second-order
phase transition line present in this theory can be interpreted as a UV phase
transition line if we allow for an anisotropic scaling of space and time.
