# Theoretical best colors for dithering

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?

--- original question ---

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.

• Hi. Welcome to GDSE What "practical applications" do you need this for? Also what does it have to do with graphic design? Why limit yourself to graphics with dithering? Commented Sep 5, 2022 at 17:41
• Your initial premise is wrong, which means whatever you do you will not achieve this. Emissive displays can get a lot closer than inks of any sort, but nothing can achieve the same light value range as the eye, nor its colossal gamut. See en.wikipedia.org/wiki/Gamut Commented Sep 5, 2022 at 17:42
• The paper below the common CMYK printing inks isn't there to provide 5th color. It's there to reflect light back. The apparent color is produced in our sight system when the inks filter out wavelength ranges. C, M and Y inks would be pretty good for many purposes, but they cannot make deep enough black. If one puts to the same place C, M and Y inks which are all transparent, they together remove a good amount of the light, but black is opaque and makes it better. You walk and also stumble along explored paths.
– user82991
Commented Sep 5, 2022 at 18:26
• Why limit myself? For the fun of it, really, but the idea I have in mind, which I won't detail, it is simply not possible not to limit. As for what this have to do with graphic design, I really don't know. I made great effort to find the right forum. This seemed the closest. Really I need physics and biology... Yes, I know about color spaces. All within reason. Commented Sep 5, 2022 at 21:32
• Also, potato potato. The paper of the paper matters. If for example it is black, you can still use CMYK, but the key will be different, as I understand it. Thus, in this scenario, CMYK is 5 colors, or there is something I don't understand at all, and there will be little hope explaining it to me. Commented Sep 5, 2022 at 21:36

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.

• I would like to point out that cyan magenta and yellow is the exact opposite of rgb for a process thats exact oppsite of rgb. Commented Sep 7, 2022 at 16:52
• I think the flip dot display as described here would not work as the opposite of RGB, because each dot needs to be exactly one of the primary colours used. In CMYK it is possible to create red by overlaying magenta and yellow, but in this flip dot display magenta and yellow would combine as a checkerboard pattern of the two colours and create pink. It would be like the dithering pattern you could get with printing 50% M and 50% Y, not like printing 100% M and 100% Y. Creating red would require flip dots which were red. RGB values would be the average of the RGB values of the flip dots. Commented Sep 8, 2022 at 9:29
• IT does not matter if things are overlaid or not its just needs a bigger dither. Commented Sep 8, 2022 at 9:30
• If you overlay magenta and yellow the subtractive mixing will remove the reflected short and medium wavelengths of light leaving just long (red) wavelengths reflected. If yellow and magenta are visible you will get medium (green) wavelengths from the yellow and short (blue) wavelengths from the magenta. The result will be more RGB 100%, 50%, 50% than RGB 100%, 0%, 0%. Commented Sep 8, 2022 at 9:37
• Well thas is true if the flipdot isnt just some sort of allegory OP clearly wants to not tell the acytual use. So your option is either to use persistence of vision or need to treat the flipdot display as a emissive source and just use colors just RGB+ black. If you have enough dots you can have more, though your maximum saturation will suffer tremendeously. since most of the screen would need to be off at most times, It would be better if each dot in fact could do atleast 3 states. Commented Sep 8, 2022 at 11:29

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.

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.

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".

• yes, indeed I have. However, It just doesn't work very well, presumably because cmyk isn't just four colors, really, as the color of the paper, is also taken into account. I my scenario, there is not paper, and the magenta is basically ruining everything. As I've hinted at, I'm rather an imbecile, when it comes to these matters, but I can judge results. I am limited to 4 colors, but really, it's the understanding part I'm interested in. I am aware of the color space complications, but we can often be fooled regardsles. Commented Sep 5, 2022 at 21:13
• I do not understand. White of the paper is the starting point of any substractive method. If you somehow want to ditch one "color" ditch the black ink. Commented Sep 5, 2022 at 22:05
• Sometimes there are limitations that are out of your control, and when that happens, you have to make due with the options you've got. It so happens that I do have options. have done extensive testing, and you can get very with, for example yellow, cyan, red and black, or even substituting the red with white. In fact, just using cyan, yellow, and black, actually works pretty well, all things considered. All I really want, is to understand the theory, so I can avoid the trial and error with literally millions of combinations. Commented Sep 5, 2022 at 23:56

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.

• Monitor rgb is not single wavelength. It would be great if it was but thats not so easy. And for a reflective surface even harder. Commented Sep 7, 2022 at 18:20
• You are right. Laser diode monitors are not especially common nor available, so the half-intensity spectral coverage of the R,G and B dots in monitors are easily 50 nanometers. Stimulated emission monochromator (dye) materials are available. They could create the lasers which are pumped by white daylight.
– user82991
Commented Sep 7, 2022 at 18:38
• Somehow it does not sound that easy. Have you tried doing this? Commented Sep 7, 2022 at 18:42
• Never. It's far beyond the possibilities of ordinary punters like me. Someone in a good academic well sheltered workplace has infinitely better possibilities. But that one cannot be there a maintenance worker, he must be one of those who are qualified to post PhD research affairs, I guess. A good maintenace worker has some possibilities to do something (firabels) interesting by hanging around them. But he must have something which makes him look irreplaceable.
– user82991
Commented Sep 7, 2022 at 19:04
• Oh and atleast one of the janitors has a PhD Commented Sep 7, 2022 at 19:33