We show by experimental measurements and theoretical analyses that there exists a pattern transition from optical modulation instability to transverse instability in nonlinear media. An input coherent beam propagating in the photorefractive crystals is observed to break up into stripe filaments at a first threshold voltage. By modeling the periodic strip filaments as cnoidal waves, we demonstrate that a second threshold voltage for forming dot filaments comes from the transverse instability, resulting in a good agreement with the experimental data.