  Stationary states of non-interacting electrons on a Koch fractal are
investigated within a tight binding approach. It is observed that if a
hierarchically long range hopping is allowed, a suitable correlation between
the parameters defining the Hamiltonian leads to spectacular changes in the
transport properties of finite, but arbitrarily large fractals. Topologically
identical structures, that are found to support the same distribution of the
amplitudes of eigenstates, are conducting in some cases and insulating in the
others, depending on the choice of the hierarchy parameter. The values of the
hierarchical parameter themselves display a self-similar, fractal character.
