SCALING AND THE FRACTAL GEOMETRY OF 2-DIMENSIONAL QUANTUM-GRAVITY

We examine the scaling of geodesic correlation functions in two-dimens ional gravity and in spin systems coupled to gravity. The numerical da ta support the scaling hypothesis and indicate that the quantum geomet ry develops a nonperturbative length scale. The existence of this leng th scale allows us to extract a Hausdorff dimension. In the case of pu re gravity we find dr approximate to 3.8, in support of recent theoret ical calculations that d(H) = 4. We also discuss the back-reaction of matter on the geometry.