I've done some development work in Pico-8, and some time ago I wrote a plugin for the Aseprite pixel art editor to convert an arbitrary image into the Pico-8 palette using Floyd-Steinberg dithering[0]
I ran their example image through it, and personally I think the results it gives were the best of the bunch https://imgur.com/a/O6YN8S2
[0] https://github.com/aquova/aseprite-scripts/blob/master/pico-...
(I don’t know how it works for others, but it has always been atrocious for me. Their server is over 200ms away, and even with uBlock Origin blocking ten different trackers it takes fully 35 seconds before it even begins to load the actual image, and the experience once it’s finished is significantly worse than just navigating directly to the image anyway. Tried it in Chromium a couple of times, 55 and 45 seconds. Seriously, imgur is so bad. Maybe it ain’t so bad in the USA, I don’t know, but in Australia and in India it’s appallingly bad. You used to be able to open the image URLs directly, but some years ago they started redirecting to the HTML in general if not loading as a subresource or maybe something about accept headers; curl will still get it directly.)
You might not thing that you'd notice that, but it looks surprisingly bad. Your eyes would immediately notice that there are "stripes" of solid gray instead of a smooth continuum. But if you apply dithering, your eyes won't be able to notice (at least not easily). It will all look smooth again.
In a situation like this, I like to use "blue noise" dithering, but there are scores of dithering methods to choose from.
CAM16-UCS looks the best because it avoids this. It gives us peach-and-pink water that matches the "feel" of the original image better. I wonder if it's designed to saturate the image to match the palette?
[0]: https://en.wikipedia.org/wiki/Floyd%E2%80%93Steinberg_dither...
If one were wanting to render an image on the PICO-8 itself, the ideal algorithm would select the best 16 colors from the full 32-color palette which, when dithered, produce the most perceptually accurate version of the original image in 128x128 pixels. Were I a smarter man I would create this, but alas.
Even if you got something very posterized like in the article I think it could at least be a great reference for a more traditional processing step afterwards. Always wonder why that doesn’t seem to exist yet.
One bottleneck of course is that the display you are on, where you are viewing the image, is likely not to have a gamut rich enough to even display all the colors of the Macbeth chart. No amount of fiddling with knobs will get you a green as rich as reality if there is an intense green outside the display's capabilities.
But of course you can try to get close.
[1] https://en.wikipedia.org/wiki/Color_chart
(I seem to recall, BTW, that these Greytag-Macbeth color charts are so consistent because they are representing each color chemically. I mean, I suppose all dyes are chemical, but I understood that there was little to no mixing of pigments to get the Macbeth colors. I could be wrong about that though. My first thought when I heard it was of sulfur: for example, how pure sulfur, in one of its states, must be the same color every time. Make a sulfur swatch and you should be able to constantly reproduce it.)
Not to mention every screen is different, so whatever changes you’re doing, even if they looked right to you in the moment, would be useless when you sent your image to your computer for further processing.
Oh, and our eyes can perceive it differently too. So now you’re doing a ton of work to badly change the colours of an image so they look maybe a bit closer to reality for a single person on a single device.
It's not perfect of course, but gets a surprisingly good result for close to zero effort.
Other systems of the time either used a simple RGBI formula with modifications (IBM, with its "CGA brown"), or a palette evenly spaced around the NTSC hue wheel (Apple II, or again the CGA in composite output mode)
Any serious attempt would involve higher level dithering to better reproduce the colours of the original image and dithering is one of those topics that goes unexpectedly crazy deep if you are not familiar with the literature.
→ https://files.catbox.moe/2uuqka.png
It's bad. :-o