  We present a numerical survey of the nonlinear flavor development of dense
neutrino gases. This study is based on the stationary, two-dimensional ($x$ and
$z$), two-beam, monochromatic neutrino line model with a periodic boundary
condition along the $x$ direction. Similar to a previous work, we find that
small-scale flavor structures can develop in a neutrino gas even if the
physical conditions are nearly homogeneous along the $x$ axis initially. The
power diffusion from the large-scale to small-scale structures increases with
the neutrino density and helps to establish a semi-exponential dependence of
the magnitudes of the Fourier moments on the corresponding wave numbers. The
overall flavor conversion probabilities in the neutrino gases with small
initial sinusoidal perturbations reach certain equilibrium values at large
distances which are mainly determined by the neutrino-antineutrino asymmetry.
Similar phenomena also exist in a neutrino gas with a localized initial
perturbation, albeit only inside an expanding flavor conversion region. Our
work suggests that a statistical treatment may be possible for the collective
flavor oscillations of a dense neutrino gas in a multi-dimensional environment.
