  We study the dynamics of an electron wave-packet in a two-dimensional square
lattice with an aperiodic site potential in the presence of an external uniform
electric field. The aperiodicity is described by $\epsilon_{\bf m} =
V\cos{(\pi\alpha m_x^{\nu_x})}\cos{(\pi\alpha m_y^{\nu_y})}$ at lattice sites
$(m_x, m_y)$, with $\pi \alpha$ being a rational number, and $\nu_x$ and
$\nu_y$ tunable parameters, controlling the aperiodicity. Using an exact
diagonalization procedure and a finite-size scaling analysis, we show that in
the weakly aperiodic regime ($\nu_x,\nu_y < 1$), a phase of extended states
emerges in the center of the band at zero field giving support to a macroscopic
conductivity in the thermodynamic limit. Turning on the field gives rise to
Bloch oscillations of the electron wave-packet. The spectral density of these
oscillations may display a double peak structure signaling the spatial
anisotropy of the potential landscape. The frequency of the oscillations can be
understood using a semi-classical approach.
