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.
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