  In infinite volume the gradient flow transformation can be interpreted as a
continuous real-space Wilsonian renormalization group (RG) transformation. This
approach allows one to determine the continuous RG $\beta$ function, an
alternative to the finite-volume step-scaling function. Unlike step-scaling,
where the lattice must provide the only scale, the continuous $\beta$ function
can be used even in the confining regime where dimensional transmutation
generates a physical scale $\Lambda_{\mathrm{QCD}}$. We investigate a pure
gauge SU(3) Yang-Mills theory both in the deconfined and the confined phases
and determine the continuous $\beta$ function in both. Our investigation is
based on simulations done with the tree-level Symanzik gauge action on lattice
volumes up to $32^4$ using both Wilson and Zeuthen gradient flow (GF)
measurements. Our continuum GF $\beta$ function exhibits considerably slower
running than the universal 2-loop perturbative prediction, and at strong
couplings it runs even slower than the 1-loop prediction.
