Theoretical best colors for dithering

Question

It would seem that I'm very bad at explaining myself. This is not unusual, thus this clarification.

Imagine a flip dot display. 2 colors, one or the other, per flip dot or pixel, no substrate, no ability to adjust the intensity. The imagine that these flip dots are infinitely small, or perceivable, individually, and that instead of just 2, you can have n colors, of your choosing. You can even play with he idea that every other flip dot or pixel, has a different set of colors, but that one I think I can figure out for my own.

And then the actual question. What is the most versatile set of colors, for at set of a given size, and how do you figure it out?

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If I am not much mistaken, given enough resolution, with just 4 colors, perhaps even less, though I don't really think so, you can simulate the appearance of any color the eye can perceive, involving the concept of dithering, to mix the colors, without actually doing so, exploiting the limitations of human vision.

I have tried various approaches, the last couple of weeks, to figure out what those color might be, from studying data on the sensitivity of the L M S cones, in the human eye, to brute force manual and automated testing.

The results vary a bit, but generally the best results seem to involve yellow, red, a very light cyan, and of course black. There is no paper or background to provide a 5th or no color, so that is rather important.

However, I have also found other option, for example involving some variant of orange and/or purple and I have so far, completely failed to draw any particularly useful conclusions. Of course, my testing has been on the computer, in the emissive space, if you can put is like that, but I do actually plan to use this knowledge, in the reflective space, for a project I'd like to work on, in the future, which further complicates matters, as I have no idea how that conversion works, even after spending days on end, reading about, among other things, that particular subject.

In short, I may well have what I need, for practical applications, but I wouldn't know, and I'd very much like to understand it too.

Answer 1

What colours to use in a flip dot display is an interesting question. I think it would work the same way as a Maxwell colour wheel, but relying on tiny dots rather than persistence of vision.

The colours could be different for emissive and reflective space due to gamut limitation, and using only four colours would significantly limit the gamut achieved, so it would depend on what subset of the gamut was most useful.

Theoretically in the RGB emissive space you would need the eight corners of the RGB cube (black, white, red, yellow, green, cyan, blue, magenta) to display the full gamut.

When working with fewer colours you need to focus on colours which are used more often at high intensity, so you need red and yellow, and then black as a base.

Presumably light cyan works as a substitute for both white and blue to expand the space (blue here not in the same sense as RGB blue, which is blue-violet). I think the range could be improved significantly by adding an additional colour and having both blue and white.

If compromise is needed to reduce the number of colours, blue does seem to be the place to do it. Early two-colour technicolor left out blue and just used red and green.

In the reflective space it gets interesting. Printing with dithering only works in CMYK because the dots can overlap and work with subtractive mixing, the same result could not be achieved with a flip dot display as you describe it.

Personally I think in the reflective space for the best gamut you would need basic black, white, red, yellow, green and blue, though if you had to do without one of those you could omit green, providing the yellow was a cool lemon yellow and the blue tended towards cyan. If you needed to limit further to four I think it would be best to combine blue and white to very light cyan as you have already found. Reflective space does not have an equivalent of sRGB to define it, the nearest you might get is Pointer's gamut, so there isn't an ideal set like the corners of an RGB cube.

What makes this idea of a reflective flip dot display interesting to me is I think it is the only type of display where the basic unique hues (psychological primary colours) would be the best set of primary colours to use, better than RGB or CMYK. I think this is due to both a flip dot display averaging colours rather than adding or subtracting, and how humans perceive colour, but I do not have hard evidence I can cite.

Edit:

Here is the relevant part of a theory I am working on. This chart shows the range of colours from analysing sRGB images of the natural environment, shown in DKL space, which is comparable to linearized sRGB. The hexagon is the sRGB gamut, and the curved shape outside of it is the MacAdam limit, which is a theoretical limit for reflective surfaces. Approximately 99% of pixels in the images lie in the area which is solidly coloured, with the remaining 1% of pixels in the areas fading to white in proportion with the number of pixels.

In DKL space, straight lines connecting the non-black primaries of your flip dot display will show the total gamut, ignoring brightness. I think the primaries that will work best are the ones which will enclose as much of the solidly coloured area as possible, which as you have found is red, yellow, and something in the blue/cyan area.

Answer 2

Have you heard of CMYK?

The 4 colors are Cyan, Magenta (not red), and yellow, with added black for depth.

It has been used in commercial printing for decades. Inkjet printers use dithering to mix the colors in different amounts given the overall size of each droplet is the same. Color laser printers use the same colors too.

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Regarding more colors. There are some printers that use more than 4 colors. Some use a variation of cyan, magenta, and black, but lighter, and those are used on light zones so the dots are less visible. But that is not relevant to your question.

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There was a printing system called hex chrome, that expanded a bit the range of reproducible colors. But the cost-benefit was not good enough. Why don't we see more of hexachrome to this day?

For specific projects you can use some other inks, like spot colors, but, again, for general purposes, a CMYK approach is the most effective one.

The inks are not perfect, but given our understanding of chemistry to create them, they are pretty good. They do not reproduce "all the colors the human eye can see". They have a limited capacity. That is what we call "color gamut" https://www.google.com/search?client=firefox-b-d&q=What+is+Color+Gamut. The concept is used in both, printed material and electronic devices.

I am not sure if you want to "discover the black thread".

Answer 3

After you inserted your flip dot model to the question the answering is easy.

Use as many single wavelength colors as you can afford plus black (=no light). Let the non-black colors be distributed evenly over the visible wavelength range. Let the first 3 of them have the same wavelengths as the peak intensity wavelengths of R, G and B in RGB displays.

You may make an insertion: "I want solid color materials, not any led lamps like displays have".

You can get them. There are numerous fluorescent solid materials which convert wide band radiation to a single wavelength. Effectively they produce the same as led lamps.

Using such materials in printing is difficult, because the dots must not overlap. If one prints say cyan ink over yellow in normal CMYK printing both inks still can do their jobs (=absorb certain wavelength range and let the others go through) Fluorescent inks cannot do it - just said that they convert wideband light to a certain wavelength; that wideband light vanishes temporarily to electron state excitations and single wavelength light is emitted when the states collapse.

Why not settle to R, G and B? By inserting more single wavelength colors you can get higher chroma intermediate colors than by mixing only R,G and B.

You may say: "What's that talk of mixing? The colors in my system are only ON or OFF, there's no brightness steps like those 0...255 in displays!!!"

You can simulate the brightness steps by having invisibly small dots and turn more or less of them to black to get effectively darker shades. It's one version of what we call dithering.

ADD due the appeared comments which call my suggestion sci-fi. It's not sci-fi, only practical engineering fiction.