How colors hide
Why does switching the green channel off make a number appear? The whole trick of the Ishihara test, explained with one plate.
Seven versions of plate 3, seven different answers
Plate 3, with its color channels switched off and on in an image editor. Under each version: what a person with moderate deutan color vision reads in it.
- As printedDeutan reads: 5
- Remove redDeutan reads: 5
- Remove greenDeutan reads: 6
- Remove blueDeutan reads: nothing
- Only redDeutan reads: 6
- Only greenDeutan reads: nothing
- Only blueDeutan reads: 5, faint
Taking color away made a number appear. The explanation lies in how eyes count color.
Screens count red, green and blue. Eyes count cones.
A screen mixes three channels: red, green and blue. The eye does not see those channels directly. It has three kinds of cones, and each cone sees a mix of all three channels.
| Cone | from R | from G | from B |
|---|---|---|---|
| L (“red”) | 0.31 | 0.64 | 0.05 |
| M (“green”) | 0.16 | 0.76 | 0.09 |
| S (“blue”) | 0.02 | 0.11 | 0.87 |
Both the “red” (L) and the “green” (M) cone get most of their signal from the green channel.
Each line is as thick as the share of the cone's signal that comes from that channel (linear RGB).
The brain compares the cones
The brain does not use the three cones one by one. It builds three signals from them: lightness (L + M), red-green (L − M) and blue-yellow (S against L + M).
A deutan or a protan has no red-green signal. What remains is lightness and blue-yellow. A tritan loses blue-yellow instead.
The brain adds and compares the cone signals. A crossed-out signal is the one a type of color blindness loses.
Plate 3 is built from three parts
- Orange arc: only the 6 uses it
- Green stroke: only the 5 uses it
- Pink loop: both use it
- Background: three olive inks
The 6 is written in red-green, the 5 in blue-yellow. Lightness is the noise: the background mixes three olives, from dark to light, scattered at random, and the figure's inks fall among them. So lightness alone shows neither number.
Drain the green, and watch the 6 appear
- Gray dots: the three olives of the background
- Orange dots: the 6's arc
- Pink rings: the loop both numbers share
- Green diamonds: the 5's stroke
Without red-green, a deutan can tell the 6's oranges from the olives only by lightness. And in lightness, the oranges are camouflaged: brighter than the dark and mid olives, but no brighter than the light one. No line across the chart puts every orange dot on one side and every olive dot on the other, so the 6 hides.
The olives get most of their lightness from the green channel, the oranges from red. Drain the green, and the olives darken much faster than the oranges. At 0%, only a handful of olive dots are as bright as the dimmest orange, and the 6 appears. Showing only the red channel as gray does the same.
Red minus green cancels the noise
Normal vision also has the red-green signal, which compares L with M. The olives' differences in lightness raise both cones together, so the comparison cancels them: in red-green, the three olives are almost the same. The oranges sit far from them, and no olive dot comes near the dimmest orange.
| normal: red-green | deutan: lightness | |
|---|---|---|
| the 6's arc | 0 | 183 |
| the shared loop | 0 | 180 |
This is the heart of the test: put the figure in a signal the person lacks, and fill the signals they have with noise.
Every plate plays with the same signals
Plate 1, demonstration: the 12 is as bright as the background to cones, but much darker to rods. So every kind of vision gets some difference, even rods alone.
Plate 10, vanishing: each orange in the 2 has a background twin. For normal vision they differ by 11 to 23 units of color difference, for a deutan by only 1 to 3.
Plate 2, transformation: a pink 3 plus orange strokes make the 8. The orange merges into the olive background for a deutan; the 3 survives because it also differs in blue-yellow.
Plate 22, classification: both digits have the lightness of the grays. Each type keeps the digit that still differs from the grays for them: deutans the red 2, protans the purple 6.
The difference is in the image
A color blind person cannot see the difference, but the difference is there. Moving it into a signal they have, like showing red as gray, makes it visible. That is the principle behind apps and glasses that recolor images for color blind people, and also their limit: they move differences around, they cannot add a missing cone.
- Deutan, strong
- Only red
Take any plate apart
Showing: Normal
What these models can and cannot tell you
The views on this site use published models of an average observer. Real people differ, the screen changes colors, and the cone signals are estimated from the screen's red, green and blue. The models show what information is lost, not exactly what any one person sees.