The term phi phenomenon is used in a narrow sense for an apparent motion that is observed if two nearby optical stimuli are presented in alternation with a relatively high frequency. In contrast to beta movement, seen at lower frequencies, the stimuli themselves do not appear to move. Instead, a diffuse, amorphous shadowlike something seems to jump in front of the stimuli and occlude them temporarily. This shadow seems to have nearly the color of the background. Max Wertheimer first described this form of apparent movement in his habilitation thesis, published in 1912, marking the birth of Gestalt psychology.
In a broader sense, particularly if the plural form phi phenomena is used, it applies also to all apparent movements that can be seen if two nearby optical stimuli are presented in alternation. This includes especially beta movement, which is important for the illusion of motion in cinema and animation. Actually, Wertheimer applied the term "φ-phenomenon" to all apparent movements described in his thesis when he introduced the term in 1912, the objectless movement he called "pure φ". Nevertheless, some commentators assert that he reserved the Greek letter φ for pure, objectless movement.
Wertheimer's classic experiments used two light lines or curves repeatedly presented one after the other using a tachistoscope. If certain, relatively short, intervals between stimuli were used, and the distance between the stimuli was suitable, then his subjects (who happened to be his colleagues Wolfgang Köhler and Kurt Koffka) reported seeing pure "objectless" motion.
However, it turns out to be difficult to demonstrate phi stably and convincingly. To facilitate demonstrating the phenomenon, 21st-century psychologists designed a more vivid experimental arrangement using more than two stimuli. In this demonstration, called "Magni-phi," identical disks are arranged in a circle and, in a rapid sequence, one of the disks is hidden in clockwise or counter-clockwise order. This makes it easier to observe the kind of shadow-like movement Wertheimer discovered. The Magni-phi demonstration is robust to changes of parameters such as timing, size, intensity, number of disks, and viewing distance.
Furthermore, the phenomenon may be observed more reliably even with only two elements if a negative interstimulus interval (ISI) is used (that is, if the periods during which the two elements are visible overlap slightly). In that case, the viewer may see the two objects as stationary and suppose unconsciously that the reappearance of the stimulus on one side means that the object previously displayed in that position has reappeared and not, as observed with beta movement, that the object from the opposite side has just moved to a new position. The crucial factor for this perception is the shortness of discontinuity of the stimulus on each side. This is supported by the observation that two parameters have to be chosen properly to produce the pure phi phenomenon: first the absolute duration of the gap on each side must not exceed about 150 ms., and second, the duration of the gap must not exceed 40% of the stimulus period.