We describe a new electrohydrodynamic phenomenon observed in inhomogeneous, nonaqueous colloidal dispersions with a spatially varying particle number concentration. In the presence of an external electric field, the dielectric constant and conductivity gradients in these systems engender fluid motion which results in the formation of patterned colloidal structures: columns, disks, and other more complicated structures. Other workers found similar effects in high conductivity systems, where the particles are dispersed in water with dissolved electrolyte. Our experimental results with barium titanate dispersed in low conductivity, apolar liquids indicate that electrical forces due to free charge and dielectric constant variations each play a role in inducing now. This pattern forming phenomenon differs from previously observed field-induced pattern formation in colloidal dispersions (e.g., colloidal string formation in electrorheological and ferrofluids) largely as a result of the induced fluid flow. A mathematical model has been developed which predicts, qualitatively, the initial now patterns encountered in our system. The theory may also help explain the formation of more complicated field-induced particle morphologies which have been reported in aqueous and nonaqueous media as well as the observation of dispersion band broadening during electrophoresis.