The discrete, sequential scanning (sampling) procedures used in electronic displays generate disturbing artifacts such as flicker, Moire-type patterns, and paradoxical motion. Application of the theory of random scanning procedures to displays can reduce these artifacts. The human retina provides an example of a system that uses randomness to avoid sampling artifacts. Though the retina performs a discrete spatial sampling of the stimulus, artifacts are not evident. For example, we do not see Moire patterns when we look at fine gratings. This is because the retinal receptors are positioned randomly, rather than in a regular array. Random sampling avoids conventional aliasing, but introduces noise. Constraints on the random sampling can banish most of the noise to the region above the Nyquist frequency, where it is easily removed by post-sampling low-pass filtering. For visual displays this means that the sampling artifacts can be traded for noise, and this noise can be placed in regions of space-time frequency for which the human visual system has little sensitivity. Here we report that artifacts, especially those associated with motion, are reduced by constrained random sequencing of horizontal scan lines. Three scan line sequencing procedures are compared: a sequential one, a single random sequence repeated, and a new random sequence on each update. The single random sequence flickered least and was :most as good as the new random sequence procedure at minimizing motion artifacts for the display of a vertical line moving horizontally.