We introduce a novel class of visual illusion -- motion pareidolia -- in which sequential presentations of random textures can trigger percepts of coherent apparent motion. In two experiments we presented observers with sequences of random 140x140 pixel arrays refreshing at 2.5Hz. In Experiment 1, observers were primed with a coherent motion pattern, such as fixed texture shifting up-and-down across frames. After 8 priming frames, the textures became completely random from frame to frame. Participants were instructed to indicate when they could no longer perceive the primed motion pattern. Participants' responses were delayed by an average of 6 frames (or 2.4 seconds). In Experiment 2, observers detected motion patterns in 6-frame sequences under different noise levels and falsely identified coherent motion in 39% of the purely random sequences. To account for this phenomenon, we propose a selective visual attention process that is biased to detect expected motion.