When using the Polar Clock live wallpaper, there are two color palettes labelled "(dynamic)": Polar Bear and Black Hole. What's dynamic about them? How long does it take to see it?
The colors of the rings will change gradually as they move around the clock. If you have seconds enabled you can see it pretty easily over the course of the minute.
Specifically, the color of the ring seems to progress through the spectrum of visible light in order from lowest frequency to highest. That is, it goes in the same pattern as a rainbow's colors: Red->Orange->Yellow->Green->Blue->Indigo->Violet (ROYGBIV). Then the cycle starts over again near the top of the clock.
That's how it looks on my phone, anyway. I'm not 100% positive if the other rings follow the same color pattern or if it's just the seconds ring, but the inner rings seem to be properly colored for their lengths (as in, at the point where the seconds ring reaches the end of one of the inner rings, they are both the same color).