  A one-dimensional lattice model with mosaic quasiperiodic potential is found
to exhibit interesting localization properties, e.g., clear mobility edges [Y.
Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this
mosaic quasiperiodic model to a two-dimensional version, and numerically
investigate its localization properties: the phase diagram from the fractal
dimension of the wavefunction, the statistical and scaling properties of the
conductance. Compared with disordered systems, our model shares many common
features but also exhibits some different characteristics in the same
dimensionality and the same universality class. For example, the sharp peak at
$g\sim 0$ of the critical distribution and the large $g$ limit of the universal
scaling function $\beta$ resemble those behaviors of three-dimensional
disordered systems.
