We present the first experimental observation of modulation instability of
partially spatially incoherent light beams in non-instantaneous nonlinear
media. We show that even in such a nonlinear partially coherent system (of
weakly-correlated particles) patterns can form spontaneously. Incoherent MI
occurs above a specific threshold that depends on the beams' coherence
properties (correlation distance), and leads to a periodic train of
one-dimensional (1D) filaments. At a higher value of nonlinearity, incoherent
MI displays a two-dimensional (2D) instability and leads to self-ordered arrays
of light spots.