Beta movement

The term Beta movement is used for the optical illusion of apparent motion in which the very short projection of one figure and a subsequent very short projection of a more or less similar figure in a different position are experienced as one figure that moves. 
The illusion of motion caused by animation and film is sometimes believed to rely on beta movement, as an alternative to the older explanation known as persistence of vision. However, there are notable differences between the short-range apparent motion that occurs in film (with little differences between successive images) and the long-range apparent motion originally described as beta movement (with bigger differences between positions of successive images).
Examples of use.
One example of the beta movement effect would be a set of LEDs, as shown at the adjacent picture. The LEDs, electronically, are individually controlled, but our eyes and brains perceive them as a snake running clockwise around the four edges of the square picture. This is also seen commonly on LED displays.
History.
Observations of apparent motion through quick succession of images go back to the 19th century. In 1833, Joseph Plateau introduced what became known as the phenakistiscope, an early animation device based on a stroboscopic effect. It was often assumed that the animation effect was due to persistence of vision in the form of afterimages on the retina or a mental process that filled in the intervals between the images.
In 1875, Sigmund Exner showed that, under the right conditions, people will see two quick, spatially separated but stationary electrical sparks as a single light moving from place to place, while quicker flashes were interpreted as motion between two stationary lights. Exner argued that the impression of the moving light was a perception (from a mental process) and the motion between the stationary lights as pure sense.
Max Wertheimer proved in 1912 that test subjects did not see anything in between the two different positions in which a figure was projected by a tachistocope at the speed that was ideal for the perception of one moving figure. He used the Greek letter φ (phi) to designate illusions of motion. At higher speeds, when test subjects believed to see both of the fast blinking figures more or less simultaneously, a moving objectless phenomenon was seen between and around the projected figures. Wertheimer supposed this "pure phi phenomenon" was a more direct sensory experience of motion. Some of these experiments involved beta movement. However, Wertheimer's work became famous (indeed it launched Gestalt psychology) due to his demonstrations of the phi phenomenon—a different illusion of apparent motion.
Wertheimer's optimal illusion of one figure motion across the interval between the figures was dubbed "β-Bewegung" by his co-worker Friedrich Kenkel in a publication with further studies in 1913.
Confusion about phi phenomenon and beta movement.
Wertheimer's pure phi phenomenon and beta movement are often confused in explanations of film and animation, but they are quite different perceptually and neither really explains the short-range apparent motion seen in film. 
In beta movement, you see two stimuli, formula_1 and formula_2, in succession, but you "perceive" the movement of a single object, formula_1, into position formula_2. In phi movement, you see the two stimuli formula_1 and formula_2 in succession, but what you "perceive" is the motion of something shadowy passing over formula_1 and formula_2. There are many factors that determine whether one will experience beta movement or the phi phenomenon in a particular circumstance. They include the luminance of the stimuli in contrast to the background, the size of the stimuli, how far apart they are, how long each one is displayed, and precisely how much time passes between them (or the extent to which they overlap in time).