Transverse pattern formation in an optical cavity containing a cloud of cold two-level atoms is discussed. We show that density modulation becomes the dominant mechanism as the atomic temperature is reduced. Indeed, for low but easily achievable temperatures the internal degrees of freedom of the atoms can be neglected, and the system is well described by treating them as linear dielectric particles. A linear stability analysis predicts the instability threshold and the spatial scale of the emergent pattern. Numerical simulations in two transverse dimensions confirm the instability and predict the spontaneous formation of honeycomb and hexagonal density structures, respectively, for the blue and red detuned cases.