What is the name of the RGB thing I want to be able to do, and what free program(s) can do it automatically? I'm gonna start this off with an... "indexed image"? If that's the proper term for it?



If this 384x144 image were actually only the top-left 192x48 pixels (I'll refer to that portion as "0,0"), I feel like the other five sections could most likely be generated by using a single automatic operation that applies the following RGB value (swaps/rotations) to all pixels in section 0,0 simultaneously:


0,1: Red -> Green -> Blue -> Red (#FFAA55 -> #55FFAA for one example)
0,2: Red -> Blue -> Green -> Red (#FFAA55 -> #AA55FF)
1,0: Green &lt;-> Blue (#FFAA55 -> #FF55AA)
1,1: Red &lt;-> Green (#FFAA55 -> #AAFF55)
1,2: Red &lt;-> Blue (#FFAA55 -> #55AAFF)


What is the name of the operation I'm looking for + what image editing programs can perform that operation? I tried Googling a bunch of things along the lines of "rgb rotate", "rgb exchange", "rgb swap", "rgb trade", etc. etc. etc. and I couldn't quickly + intuitively find anything that did what I wanted it to do in a single swing. The amount of stuff completely unrelated to what I had in mind that came up honestly quickly got really frustrating. I even tried Googling "triadic rotation" and nothing related to what I had in mind showed up on the 1st page.

The reason for the sorted colors instead of an actual image is basically the same reason I have to ask this question in the first place; I can't do it automatically with the free tools that I'm currently aware of the existence of.

I had to sort those 64 colors manually 6 times over with paint.net; which thankfully has functions that made it slightly easier to do, though there's definitely no way that I could quickly apply the effect I'm talking about to any actual image of any kind using paint.net (unless it has some feature I'm not yet aware of). I'm pretty sure there should be a way to apply that effect automatically; I just don't know the name of that effect + therefore can't even search for it.

One thing that came up a few times during my failed attempts at searching was "hue rotation"; however as far as I know + could observe that not only applies to only one hue range at a time, but also pays more attention to hue angle than actual RGB values (if that makes any sense). So I really don't think hue rotation is what I'm looking for; though if it's suggested to me anyway I will try it again as long as I'm given specific instructions on how to use it to achieve the effect that I desire.

If I'm not using a tag that I should be using, or even outright posting on the wrong Stack Exchange site for the question; please let me know.
Swapping color channels is called channel swap or swizzling. (Searching for "RGB channel swap" brings up lots of relevant results.) Looking at your image, the squares in the right half appear to be flipped across the diagonal.

Most editing apps have a channel mixer tool that allows you to calculate each output color channel as some combination of the input color channels. In Photoshop it's called "Channel Mixer". I've also seen it referred to as "Color Operations" or just "Color Ops". 

The flipping can usually be done with a horizontal flip followed by a vertical flip.