Illusions / Müller-Lyer
Müller-Lyer illusion
Two equal lines. One looks longer.
Measured from the image
Sliders
Make your own Müller-Lyer image
How the effect works
Two horizontal lines look different in length. Outward-pointing fins end the upper line, which looks longer. Inward-pointing fins end the lower line, which looks shorter. The main lines, called shafts, have exactly the same length.
The build script measures each shaft in pixels and prints both values side by side. They match. The script also measures the full extent of each figure, fins included. The outward-fin figure spans more space overall. One reading of the effect says you judge the whole figure and not the shaft alone, so the wider span wins.
Shorten the fins and the gap between the two extents shrinks. Set the fin length to zero and the fins vanish. Both lines become plain bars of equal length, and the illusion has nothing to work with. The sweep table steps the fin length from nothing to its maximum and shows the extent of each line at every step. Change the fin angle to compare sharp fins with wide ones. Hold a ruler against your screen if you doubt the match. The shafts agree.
Measured at the default settings
Image size: 368 by 250 px. The build script read these values from the rendered pixels.
- Shaft Length Top Px
- 240
- Shaft Length Bottom Px
- 240
- Top
- y 75, x0 64, x1 304
- Bottom
- y 175, x0 64, x1 304
- Extent Top Px
- 327
- Extent Bottom Px
- 240
Where the effect weakens
The table sweeps Fin length (px); 0 removes the fins and the illusion and scores a geometric proxy from 0 to 1: Extent difference between the two lines, as a share of half the shaft length. The proxy comes from the image geometry. The proxy measures geometry and not perception. Your own eyes decide what you see. Rows below 0.5 are marked weak.
Weak range: 0 to 30 px. Proxy at the default setting: 0.725.
| fin (px) | Proxy | Shaft Top Px | Shaft Bottom Px | Extent Top Px | Extent Bottom Px |
|---|---|---|---|---|---|
| 0 | 0 (weak) | 240 | 240 | 240 | 240 |
| 10 | 0.142 (weak) | 240 | 240 | 257 | 240 |
| 20 | 0.292 (weak) | 240 | 240 | 275 | 240 |
| 30 | 0.433 (weak) | 240 | 240 | 292 | 240 |
| 40 | 0.575 | 240 | 240 | 309 | 240 |
| 50 | 0.725 | 240 | 240 | 327 | 240 |
| 60 | 0.867 | 240 | 240 | 344 | 240 |
| 70 | 1 | 240 | 240 | 361 | 240 |
| 80 | 1 | 240 | 240 | 379 | 240 |
| 90 | 1 | 240 | 240 | 396 | 240 |
| 100 | 1 | 240 | 240 | 413 | 240 |
Try this
- Set the fin length to zero. Confirm both lines look equal.
- Raise the fin length step by step. Note where the difference becomes obvious to you.
- Change the fin angle with the fin length fixed. Compare sharp fins with wide ones.
History
- Franz Carl Müller-Lyer devised the illusion in 1889. The journal is reported differently by different sources, so the site does not name one. Source
Only facts confirmed against a source appear here. Where sources disagree, this site leaves the detail out.
More illusions
Entertainment only. Not a vision or health test.