Let's say you have six little toy boats. Since you have nothing better to do, you stack them in order of hue.
Lay them out from the bottom, three boats, two deep.
Hey, they ended up with pairs of complementary colors! Gather them up.
Lay them out again.
Not very interesting. Gather them up again.
Lay them out again.
Oh, it's red, green, blue primaries on top and cyan, magenta, yellow primaries below. Gather them up again.
...and we have reversed the stack.
1. Let's Analyze This
Start by numbering the boats, from bottom to top, so red is 1, yellow is 2, and so on. Our starting position is (1 2 3 4 5 6). Laying out the boats gets us:
((4 5 6),(1 2 3))
...and gathering up gets us (3 6 2 5 1 4). We can repeat the process by just reapplying that permutation. From the start:
(1 2 3 4 5 6)
(3 6 2 5 1 4)
(2 4 6 1 3 5)
(6 5 4 3 2 1)
Here we have reversed the order of the boats.
(4 1 5 2 6 3)
(5 3 1 6 4 2)
(1 2 3 4 5 6)
Three applications later we're back to the start.
2. Visualize It
There's an excellent permutation visualizer that can show you how the boats move[a] by Nat Alison[b].
3. Summary
I don't really know where I was going with this, but that's what you can do with six rainbow-colored toy boats.