Subtle quantum interference effects in one-dimensional quasicrystals are re
ported. Quite opposite to their metallic counterparts, quasiperiodic system
s are shown to exhibit interesting variations of their conducting propertie
s upon disruption of their long-range order. A sudden phason change in the
structure leads to a series of transitions that proceed from extremely simp
le and regular to highly complex self-similar resistive patterns.