Applications of dc electric field across parallel plate electrodes filled with an aqueous dispersion of carbon nanotubes produce slowly changing, geometrically regular patterns over the anode surface. The pattern is made visible by nonuniform concentration distributions of black-colored carbon nanotubes. Temporal developments of the pattern can be categorized to the cell pattern appearing soon after the application of the field and the butterfly pattern that follows the cell pattern. An existence of a threshold voltage and the electrode separation dependence on the cell polygon size indicate that the cell pattern is formed by electroconvection induced by electrolysis of water. In contrast, the butterfly pattern does not show the same dependencies and is a characteristic of the nanotube dispersion. Furthermore, it depends on the direction of the electric field relative to gravity, suggesting that it involves a new lateral force that has never been reported.