  Several variants of the classic Fibonacci inflation tiling are considered in
an illustrative fashion, in one and in two dimensions, with an eye on changes
or robustness of diffraction and dynamical spectra. In one dimension, we
consider extension mechanisms of deterministic and of stochastic nature, while
we look at direct product variations in a planar extension. For the pure point
part, we systematically employ a cocycle approach that is based on the
underlying renormalisation structure. It allows explicit calculations,
particularly in cases where one meets regular model sets with Rauzy fractals as
windows.
