Brief apparent motion sequences were introduced into a dynamic visual dot display by spatially shifting selected dots between successive frames. This causes the display to look as if it is drifting continuously in one direction. When such a display is observed with an interocular delay the drifting dots appear to be displaced in depth, even though there is no conventional retinal disparity in the display. We found that the magnitude of this depth shift increased with the duration of the apparent motion sequences. With sequences of five or more frames duration the depth effect was very similar to that which would have been predicted with a continuously moving target. With briefer sequences the size of the depth effect decreased rapidly. We suggest that apparent motion cascades form the basis of Tyler's dynamic visual noise stereophenomenon, and we question his “random spatial disparity” hypothesis.