  We show experimental and numerical evidence of spontaneous
self-symmetrization of focused laser beams experiencing multi-filamentation in
air. The symmetrization effect is observed as the multiple filaments generated
prior to focus approach the focal volume. This phenomenon is attributed to the
nonlinear interactions amongst the different parts of the beam mediated by the
optical Kerr effect, which leads to a symmetric redistribution of the wave
vectors even when the beam consists of a bundle of many filaments.
