Why do wheels seem to spin backward on film?

A film is a series of still snapshots taken at regular intervals, not continuous motion. When a spoked wheel turns almost the whole distance to the next spoke between two frames, the brain matches each spoke to the nearest spoke in the following frame. That nearest match lies behind it, so the wheel appears to turn backward. The effect is called the wagon-wheel effect, and it is a case of temporal aliasing. [1] [2]

One demonstration describes two cases. If each spoke moves one-quarter of the gap between spokes from frame to frame, the closest match is forward and the wheel looks like it turns forward. If each spoke moves two-thirds of the gap, the closest match is a one-third step backward, so the wheel looks like it turns in reverse. The effect relies on beta movement: motion is seen between similar objects at different positions and times, and spokes are nearly identical. [1] [2]

Plus Maths gives a numerical version. If a wheel advances 30 degrees clockwise per frame, it looks clockwise. If it advances 300 degrees clockwise per frame, that is the same as 60 degrees anticlockwise, and because the brain takes the shortest angle, the wheel appears to run in reverse. [3]

The same logic explains wheels that look frozen or slow. Wikipedia's example is a 12-spoke wheel turning twice per second, filmed at 24 frames per second. Each frame shows the spokes in the same places, so the wheel looks stationary, even though a different spoke occupies each position. Slightly slower, and the spokes fall a little behind each frame, so the wheel seems to turn backward. A clock analogy makes it concrete: photographing a second hand every 59 seconds looks backward, every 60 seconds looks frozen, and every 61 seconds looks like slow forward motion. [4] [5]

It is not limited to wagons. Helicopter rotors, aircraft propellers and car rims show it too, as does any rotating wheel lit by flickering light. [2]

Some researchers report a version of the effect under continuous light, with no camera involved. Live Science describes two competing explanations. One says the visual cortex processes input in temporal packets, like a movie camera taking snapshots. The other points to an experiment in which two identical adjacent wheels were reported as switching direction independently. A single shared frame rate would not predict that, so these scientists favor perceptual rivalry, where the brain generates two interpretations of an ambiguous scene. [6]

George Mather's demonstration takes a more skeptical line. It says claims of the effect in natural scenes probably confuse two separate phenomena with different explanations. It also notes that it is debatable whether the film effect is an illusion at all, since any system sampling rapid motion in discrete frames would be prone to it. The results do not settle the question, and the continuous-light explanation remains open. [1]