  We present a real-space renormalization group transformation with continuous
scale change to calculate the continuous renormalization group $\beta$ function
in non-perturbative lattice simulations. Our method is motivated by the
connection between Wilsonian renormalization group and the gradient flow
transformation. It does not rely on the perturbative definition of the
renormalized coupling and is also valid at non-perturbative fixed points.
Although our method requires an additional extrapolation compared to
traditional step scaling calculations, it has several advantages which
compensates for this extra step even when applied in the vicinity of the
perturbative fixed point. We illustrate our approach by calculating the $\beta$
function of 2-flavor QCD and show that lattice predictions from individual
lattice ensembles, even without the required continuum and finite volume
extrapolations, can be very close to the result of the full analysis. Thus our
method provides a non-perturbative framework and intuitive understanding into
the structure of strongly coupled systems, in addition to being complementary
to existing lattice determinations.
