  Exotic tiling patterns of quasicrystals have motivated extensive studies of
quantum phenomena such as critical states and phasons. Nevertheless, the
systematic understanding of the Landau levels of quasicrystals in the presence
of the magnetic field has not been established yet. One of the main obstacles
is the complication of the quasiperiodic tilings without periodic length
scales, thus it has been thought that the system cannot possess any universal
features of the Landau levels. In this paper, contrary to these assertions, we
develop a generic theory of the Landau levels for quasicrystals. Focusing on
the two dimensional quasicrystals with rotational symmetries, we highlight that
quasiperiodic tilings induce anomalous Landau levels where electrons are
localized near the rotational symmetry centers. Interestingly, the localization
length of these Landau levels has a universal dependence on n for quasicrystals
with n-fold rotational symmetry. Furthermore, macroscopically degenerate zero
energy Landau levels are present due to the chiral symmetry of the rhombic
tilings. In this case, each Landau level forms an independent island where
electrons are trapped at given fields, but with field control, the interference
between the islands gives rise to an abrupt change in the local density of
states. Our work provide a general scheme to understand the electron
localization behavior of the Landau levels in quasicrystals.
