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Then give us both. fast_decent_colormap() and slow_better_colormap() and hide away all your fancy maths.

Give me some images and the kinds of transforms each color space is good at, and let me pick one, already implemented in a library in a couple different languages.

What's the best color space if I want pretty gradients between 2 arbitrary colors?

What's the best color space if want 16 maximally perceptually unique colors?

What color space do I use for a heat map image?

What color space do I use if I want to pick k-means colors from an image or down sample an image to 6 colors?

This is a category error question and that's what makes these hard to answer. There's very good & clear answers, but you see the reaction to them in this thread. I wish I could share the tools I made these problems visible at BigCo, and thus easy to resolve, but alas.

TL;DR: A color space just tells you where a color is in relation to others. From there, focus on your domain (eg. mine was "~all software", 2D phone apps) and apply. Ex. the gentleman above talking about specularity and CAM16 is wildly off-topic for my use case, but, might be crucially important for 3D (idk). In general, it's bizarre to be using something besides CAM16, and if that's hard to wrap your mind around, fall back to Lab*, (HCL) and make sure you're accounting for gamut mapping if you're changing one of the components.

Is it a category error? I can see that if I blend linearly in one color space vs another space I'll get a different result. And if a try to cluster colors using one color space vs another I'll get different results. Surely the color space is relevant and my questions aren't completely non-sensical?

CAM16 can't be the best answer to all of them, can it? It's possible but I'd think some color spaces are better suited for some tasks than others.

Which CAM16 are we even talking about? A quick Google reveals CAM16 UCS, SCD and LCD.

CIELAB I've heard good things about but then OKLAB became all the rage and now I don't know what's better.