The 1968 animated Beatles movie Yellow Submarine is famed for its trippy visuals, but one detail is of particular interest. I look for this each of the umpteen times I’ve watched the movie. A square box is colored red in one frame and green in the next frame, switching colors back and forth faster than the eye can follow, making the eye perceive a simultaneous superposition of the two colors.
If you mix red and green paint, you get mud. Not a clear brown, just dull muddiness.
Red light blended with green light makes yellow light.
Certain tricks with the optic nerve called “impossible colors” are made by viewing one color through the afterimage of another color.
The redgreen box in Yellow Submarine appears as none of the above. The viewer is conscious of seeing both colors simultaneously, not blended but still distinct red and green.
OK, something different is going on here. I’d love to understand it better. Imagine with me if it were black and white squares alternating with each frame, the eye would see a smooth gray—don’t you think so? What if it were alternating yellow and blue, would they blend into green or remain yellow and blue? I’m not sure. What if three colors alternated red, blue, yellow? Or red, blue, green? I imagine white alternating with green would make a smooth brighter green. White alternating with red would appear pink. Yet red and green somehow resist appearing blended. This calls for further experimentation. I’d hope such research has already been done by now. I’m not the first person to think of it. But in 55 years of commentary on that movie, I’ve never heard anyone else mention the redgreen box.
Of course this isn’t literal quantum superposition in the physics sense, but it seems to me a more effective way to make a visual representation of quantum superposition than anything else I can think of.
Your question raises an interesting point – not about “quantum superposition”, but about color mixing.
It has long been known (since at least 165 CE) that rapidly rotating a wheel with various colors on it will “mix” the colors in the same way that mixing the pigments themselves will, so a disc with half red and half blue will appear purple. Or a disc with six colors will appear white or gray (“Newtron’s disc”)
But having alternating colors, or alternating black and white 8frames on a piece of film doesn’t result in such mixing, but your brain’s registering both. This effect was used a lot in animation – not just in Yellow Submarine, but in a lot of earlier animation, as well. Look at the shimmering of the Blue Fairy’s magic in Disney’s 1940 Pinocchio, for instance
Or the rapid changes from black to white in Koko’s Earth Control (1928)
The only difference between a rapidly rotating color disc and a piece of film is that the film gives discrete steps at a given rate. Clearly the rate is too slow for the blending to occur. That 24 frames per second that’s enough to blur motion obviously isn’t fast enough to prevent us from seeing individual changes in motion.
Stop-motion animators knew about this for a long time. They called the effect “strobing”, because it resembles the way flashes from a strobe lamp appear to successively “freeze” motion. So when Ray Harryhausen animates a flapping pterodactyl’s wings, they look unnatural because we can perceive that the wings are not moving smoothly (which would give a blu=rred image o n each frame), but stopping at each frame. Some animators tried to avoid this by moving the wings during exposure, so they blur. Steven Spielberg computer-blurred images of the rotating kiniature vflying bicycles in E.T., a process they called “Go Motion”. Modern computer CGI automatically blurs motio n to avoid strobing.
I don’t know how fast the frame rate has to be in order to eliminate the visibility of sucesive different-colored framnes, orv to avcoid “strobin”. Someoine has probably studied this, but I’m not aware of the studies. I’ll have to see if I can find anything.
I see what you mean. The alternating black and white nearly merged into gray, but not quite. If they had merged into smooth gray, there would have been no flashing effect.
What if red and green were alternated fast enough to blend instead of flash, what would it look like?
Funk & Wagnalls Unabridged Dictionary of the English Language, (1941 edition) had a chart for the Newton Disc, and a large page with hundreds of colors and the necessary proportions you need to produce that on the disc. You had to make your own Newton Disc, though.
Tangential to this, mathematician Matt Parker demonstrates >here< how a digital photograph is actually a spreadsheet. Each pixel is 255 levels of red, green or blue. He actually went through the trouble of analyzing the bit levels of each pixel in his selfie, then put those values in corresponding spreadsheet cells to make an “Excelfie.”
The only reason it looks different from pure yellow light is because the rate of alternation isn’t high enough. At a high enough rate, you wouldn’t notice the difference.
Consumer-level DLP projectors use a rotating color wheel to achieve color with a single display chip. As in, you see the red version of the image, then the green version, then the blue version. It cycles between these at a high enough rate that most people can’t tell the difference, but a few people are more sensitive and do notice.
However, if they upped the rate to, say, 1000 images/second, nobody could tell. It would just look like any other color.
So I said upthread. The question is – what’s the breakeven point at which you don’t notice the cycling? It’s probably a lot less than 1000 frames per second. But more than 24.
First-gen DLP projectors had their color wheel rotating at 60 Hz, and each of RGB got one segment of that, so yellow light was roughly 5 ms of green, 5 ms of red, then 5 ms black. That was very noticeable to me.
Later-gen DLP systems upped the rate to 120 Hz, which definitely helped, but they still had a bit of shimmer to them. I think most of the problem was due to the eye’s saccades–the involuntary movements that shift your vision around as you look at something. The trouble is that you end up seeing a different-colored snapshot as your eyes move, and so the edges don’t quite line up and there’s a rainbow effect. I didn’t notice a problem with a large field of color.
So it depends on the use case I’d say. Probably 120 Hz is enough as general illumination. And enough for a movie, for most people, most of the time. But you’d probably have to get to 240 Hz or so for it to be totally unnoticeable under all conditions. And that’s 240 Hz of RGB cycles–it’s really more like 720 Hz if you’re counting the frames separately.
I recall a wheel that was solid black on one side, the other half white with a spiral stepping of 3 black squares (or wedge elements, not literal squares) which when spun produced a sort of beige.
Color, though, is a pretty complicated thing that is more than just your HSV/RGB/CMYK/whatever. The elements of luminance and highlight and contrast position (relative to an adjacent shade, cf dithering) make identifying a particular color challenging.
It’s not just beige that it produces; it’s the whole rainbow (though fairly desaturated). Not exactly related to the question here, but an interesting illusion nevertheless.
I believe the perception of alternating colors appearing as 1 color occurs when the rate of alternation exceeds the flicker fusion threshold (psycophysics of vision). This threshold can vary between different individuals, conditions (e.g. fatigue, metabolic rate), and between species.
It’s just another trick our imperfect brains play on us. I’m cool with that. A perfect brain (one that perceives reality as it really is) could cause insanity.
So it’s clear that my error in the OP was “faster than the eye can see.” Frame rates are fast enough to give the illusion of smooth movement, but the eye can still distinguish rapidly flashing colors.