We show that the surface roughness for $c<1$ matter theories coupled to $2D$ quantum gravity is described by a self-similar structure of baby universes. There exist baby universes whose neck thickness is of the order of the ultraviolet cutoff, the largest of these having a macroscopic area $\sim A^{ 1 \over { 1-\gamma}}$, where $A$ is the total area and $\gamma$ the string susceptibility exponent.
Categories: hep-th