  We investigate the properties of electronic states in two and
three-dimensional quasiperiodic structures: the generalized Rauzy tilings.
Exact diagonalizations, limited to clusters with a few thousands sites, suggest
that eigenstates are critical and more extended at the band edges than at the
band center. These trends are clearly confirmed when we compute the spreading
of energy-filtered wavepackets, using a new algorithm which allows to treat
systems of about one million sites. The present approach to quantum dynamics,
which gives also access to the low frequency conductivity, opens new
perspectives in the analyzis of two and three-dimensional models.
