Freeze a moving wheel
Keep the wheel turning at 40 rpm. Change only the camera rate until the unmarked spokes stand still.
Find a rate where each frame catches the next spoke.
THE MISSING FRAMES / A 5-MINUTE EXPERIMENT
A wheel turns forward at 40 rpm.
On camera, it turns backward at 10.
Twelve identical spokes. Ten pictures a second. Nothing reverses except the story the pictures tell. Press play, then change what the camera captures.
Known motion
+40 rpm
clockwise
Camera snapshots
-10 rpm
shortest-step reading: backward
t = 0.00 s
The left dot tracks a known spoke. The camera sees identical spokes until you add a mark.
0 rpm120 rpm
2 fps30 fps
At 40 rpm, try:
↶
01
Find the missing turn.
Each little wheel is an actual computed snapshot. Select one to compare it with the next. The camera records positions; the movement between them is missing.
Frames 0 and 1
+24°real movement per frame
-6°shortest matching step
A unique mark lets you follow the same spoke instead of mistaking it for its neighbour.
02
Same pictures. Different realities.
Could these six frames prove which way the wheel turned? Try all three speeds. This example always uses 12 unmarked spokes and 10 fps.
The gap is 50 rpm.
In the fixed example, an extra 50 rpm adds exactly one spoke spacing between pictures. Every snapshot stays the same. Even infinitely many frames at this same rate cannot separate these constant speeds.
“Looks slowest” is an assumption.
Our readout picks the smallest turn that fits each pair. It is a plausible interpretation, not proof of the real speed. This ambiguity is called aliasing.
03
Give the camera better evidence.
Three small challenges. Load one, use the controls above, then check your result here. Each starts at 40 rpm, 12 spokes and 10 fps.
0 of 3 experiments completed
Recover the direction
Keep 40 rpm and 12 unmarked spokes. Find the lowest whole-number frame rate that gives the correct shortest-step speed.
Exactly half a spoke per frame still leaves two possible directions.
Break the symmetry
Keep 40 rpm, 12 spokes and 10 fps. Add a unique mark and make the shortest-step reading track the real movement.
You can change the evidence without changing the camera rate.
More than 16 fps
Changing the shutter is different.
A longer exposure smears movement inside a frame; a higher frame rate records more positions. Blur can soften aliasing, but it does not create the missing sharp snapshots.
What this experiment models
All values and frames are calculated here, not measured. Clockwise is positive. The camera takes instantaneous, equally spaced snapshots of rigid, evenly spaced spokes. No motion blur or rolling-shutter distortion is modeled. Playback follows simulation time; device refresh rates can affect how smooth it looks. Step through frames for the exact evidence.
Open the calculation and all 12 current frames
Spoke spacing = 360 / spoke count. Real step = 6 × rpm / fps degrees. With a unique mark, the repeat angle is 360 degrees; otherwise it is one spoke spacing. Subtract whole repeat angles until the step is between minus and plus half a repeat. At exactly half, both directions fit equally well.
Shortest-step rpm = step × fps / 6. This rule gives the true speed only when the real step is strictly smaller than half a repeat. It is a nearest-position tracking rule for this ideal wheel, not a claim that a sharp image has no higher spatial harmonics.
| Frame | Time (s) | Real angle (°) | Repeat phase (°) |
|---|
Sources and further exploration
- UC Davis, Temporal Aliasing: The Wagon Wheel Effect (Winter 2026). Sampled positions, apparent reversal and the ambiguous halfway case.
- TU Delft, MUDE: Sampling (2025 textbook). Repeated spokes and information lost between samples.
- MIT, Foundations of Computer Vision: Image Sampling and Aliasing, section 20.6. Temporal aliasing, filtering and global versus rolling shutters.