  We analyze the spreading of wavepackets in two-dimensional quasiperiodic and
random tilings as a function of their codimension, i.e. of their topological
complexity. In the quasiperiodic case, we show that the diffusion exponent that
characterizes the propagation decreases when the codimension increases and goes
to 1/2 in the high codimension limit. By constrast, the exponent for the random
tilings is independent of their codimension and also equals 1/2. This shows
that, in high codimension, the quasiperiodicity is irrelevant and that the
topological disorder leads in every case, to a diffusive regime, at least in
the time scale investigated here.
