  Numerical simulations of the recently derived fully nonlinear equations of
motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf
71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which
show the spontaneous formation of a single extreme wave on the deep water. This
rogue wave behaves in an oscillating manner and exists for a relatively long
time (many wave periods) without significant change of its maximal amplitude.
