Stereoscopic 3D (S3D) display is beneficial for educational purposes, although visual fatigue remains an issue for practical use. To avoid this, we have introduced an intermittent S3D exposure method. In order to clarify detailed effects of pictorial cues in 2D and S3D, this study introduces a rotating lines perception test, in which the random rotational motion of two lines provides pictorial cues in non-S3D. In the test, participants are asked to distinguish depths of the lines after rotation with and without S3D display. Sequences of perception scores were translated into a one-dimensional walk. The perception trajectories of low success rates were found to be similar to Brownian motion, and trajectories of higher success rates showed negatively correlated fluctuations, implying the suppression of failures. Introduction of S3D led a shift from non to negatively correlated fluctuations. Further, small angle-rotation was found to affect perception with high scores. This effect was reduced by S3D. Finally, small depth-separation was found to remain an evident factor of misperception, even under S3D. These results suggest that non-S3D works well if the viewer is sufficiently careful