  We study $q=10$ and $q=200$ state Potts models on dynamical triangulated
lattices and demonstrate that these models exhibit continuous phase
transitions, contrary to the first order transition present on regular
lattices. For $q=10$ the transition seems to be of 2nd order, while it seems to
be of 3rd order for $q=200$. For $q=200$ the phase transition also induces a
transition between typical fractal structures of the piecewise linear surfaces
corresponding to the triangulations. The typical surface changes from having a
tree-like structure to a fractal structure characterizing pure gravity when the
temperature drops below the critical temperature. An investigation of the
alignment of spin clusters shows that they are strongly correlated to the
underlying fractal structure of the triangulated surfaces.
