  We perform numerical simulations of fast collective neutrino flavor
conversions in an one-dimensional box mimicking a system with the periodic
boundary condition in one spatial direction and translation symmetry in the
other two dimensions. We evolve the system over several thousands of the
characteristic timescale (inverse of the interaction strength) with different
initial $\bar\nu_e$ to $\nu_e$ number density ratios and different initial seed
perturbations. We find that small scale structures are formed due to the
interaction of the flavor waves. This results in nearly flavor depolarization
in a certain neutrino phase space, when averaged over the entire box.
Specifically, systems with initially equal number of $\nu_e$ and $\bar\nu_e$
can reach full flavor depolarization for the entire neutrino electron lepton
number ($\nu$ELN) angular spectra. For systems with initially unequal $\nu_e$
and $\bar\nu_e$, flavor depolarization can only be reached in one side of the
$\nu$ELN spectra, dictated by the net neutrino $e-x$ lepton number
conservation. Quantitatively small differences depending on the initial
perturbations are also found when different perturbation seeds are applied. Our
numerical study here provides new insights for efforts aiming to include impact
of fast flavor conversions in astrophysical simulations while calls for better
analytical understanding accounting for the evolution of fast flavor
conversions.
