  We exactly solve a special matrix model of dually weighted planar graphs
describing pure two-dimensional quantum gravity with an R^2 interaction. It
permits us to study the intermediate regimes between the gravitating and flat
metric. Flat space is modeled by a regular square lattice, while localised
curvature is introduced through lattice defects. No ``flattening'' phase
transition is found with respect to the R^2 coupling: the infrared behaviour of
the system is that of pure gravity for any finite R^2 coupling. In the limit of
infinite coupling, we are able to extract a scaling function interpolating
between pure gravity and a dilute gas of curvature defects on a flat
background. We introduce and explain some novel techniques concerning our
method of large N character expansions and the calculation of Schur characters
on big Young tableaux.
