  A search strategy for asymptotic safety is put forward and tested for a
simplified version of gravity in four dimensions using the renormalization
group. Taking the action to be a high-order polynomial of the Ricci scalar, a
self-consistent ultraviolet fixed point is found where curvature invariants
become increasingly irrelevant with increasing mass dimension. Intriguingly,
universal scaling exponents take near-Gaussian values despite the presence of
residual interactions. Asymptotic safety of metric gravity would seem in reach
if this pattern carries over to the full theory.
