  We study renormalization group equations of quantum gravity in four
dimensions. We find an ultraviolet fixed point in accordance with the
asymptotic safety conjecture, and infrared fixed points corresponding to
general relativity with positive, vanishing or negative cosmological constant.
In a minisuperspace approximation, we additionally find a renormalization group
limit cycle shielding the ultraviolet from the infrared fixed points. We
discuss implications of this pattern for asymptotically safe gravity in the
continuum and on the lattice.
