  In systems near phase transitions, macroscopic properties often follow
algebraic scaling laws, determined by the dimensionality and the underlying
symmetries of the system. The emergence of such universal scaling implies that
microscopic details are irrelevant. Here, we locally investigate the scaling
properties of the metal-insulator transition at the LaAlO3/SrTiO3 interface. We
show that, by changing the dimensionality and the symmetries of the electronic
system, coupling between structural and electronic properties prevents the
universal behavior near the transition. By imaging the current flow in the
system, we reveal that structural domain boundaries modify the filamentary flow
close to the transition point, preventing a fractal with the expected universal
dimension from forming. Our results offer a generic platform to engineer
electronic transitions on the nanoscale.
