  We study the properties of the one-dimensional Fibonacci chain, subjected to
the placement of on-site impurities. The resulting disruption of
quasiperiodicity can be classified in terms of the renormalization path of the
site at which the impurity is placed, which greatly reduces the possible amount
of disordered behavior that impurities can induce. Moreover, it is found that,
to some extent, the addition of multiple, weak impurities can be treated by
superposing the individual contributions together and ignoring nonlinear
effects. This means that a transition regime between quasiperiodic order and
disorder exists, in which some parts of the system still exhibit
quasiperiodicity, while other parts start to be characterized by different
localisation behaviours of the wavefunctions. This is manifested through a
symmetry in the wavefunction amplitude map, expressed in terms of conumbers,
and through the inverse participation ratio. For the latter, we find that its
average of states can also be grouped in terms of the renormalization path of
the site at which the impurity has been placed.
