We have used information-theoretic measures to compute the amount of dependency which exists between two and three gradient directions at separate locations in an ensemble of natural images. Control experiments were performed on other image classes: phase randomized natural images, whitened natural images and Gaussian noise images. The results show that, for an ensemble of natural images, the amount of 2-point and 3-point gradient direction dependency is equivalent to its ensemble of phase randomized natural images. Therefore, we conclude that the amount of gradient direction dependency in an ensemble of natural images is determined by the ensemble's mean power spectrum rather than the phase spectra of the images. Moreover, this relationship does not extend to individual natural images, the amount of dependency between gradient magnitudes, or gradient directions at high gradient magnitude locations.