  The quest for the topological phases of matter in an aperiodic system has
been greatly developed recently. Here we investigate the effects of disorder on
topological phases of a two-dimensional Ammann-Beenker tiling quasicrystalline
lattice. For comparison purposes, we also consider the case of a periodic
snub-square crystalline lattice, which has the same primitive tiles as the
Ammann-Beenker tiling quasicrystalline lattice. By calculating the spin Bott
index and the two-terminal conductance, we confirm that the topological phases
with disorder share the similar properties in the two systems which possess
different symmetry and periodicity. It is shown that the quantum spin Hall
states are robust against weak disorder in both the quasicrystalline lattice
and the crystalline lattice. More interesting is that topological Anderson
insulator phases induced by disorder appear in the two systems. Furthermore,
the quantized conductance plateau contributed by the topological Anderson
insulator phase is verified by the distribution of local currents.
