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We study pattern formation in a model of cyanobacteria motion recently proposed by Galante, Wisen, Bhaya and Levy. By taking a continuum limit of their model, we derive a novel fourth-order nonlinear parabolic PDE equation that governs the behaviour of the model. We then derive the instability thresholds for the onset of pattern formation. We also compute analytically the spatial profiles of the steady state aggregation density. These profiles are shown to be of the form sech p where thedoi:10.1088/0951-7715/29/10/3174 fatcat:gi3p2snpfrcf5fzi2mwq4a2oxy