  We consider quantum wave propagation in one-dimensional quasiperiodic
lattices. We propose an iterative construction of quasiperiodic potentials from
sequences of potentials with increasing spatial period. At each finite
iteration step the eigenstates reflect the properties of the limiting
quasiperiodic potential properties up to a controlled maximum system size. We
then observe approximate metal-insulator transitions (MIT) at the finite
iteration steps. We also report evidence on mobility edges which are at
variance to the celebrated Aubry-Andre model. The dynamics near the MIT shows a
critical slowing down of the ballistic group velocity in the metallic phase
similar to the divergence of the localization length in the insulating phase.
