We propose a novel platform to flexibly synthesize any arbitrary meaningful facial expression in the absence of actor performance data for that expression. With techniques from computer graphics, we synthesized random arbitrary dynamic facial expression animations. The synthesis was controlled by parametrically modulating Action Units (AUs) taken from the Facial Action Coding System (FACS). We presented these to human observers and instructed them to categorize the animations according to one of six possible facial expressions. With techniques from human psychophysics, we modeled the internal representation of these expressions for each observer, by extracting from the random noise the perceptually relevant expression parameters. We validated these models of facial expressions with naive observers.