NeoPixels are all about color - beautiful, vibrant, in some cases retina-scorching, color.  But this project is supposed to be a clock, not a beacon for alien spacecraft entering orbit.  I want a color palette that's interesting over a 24-hour period but not extreme or overwhelming.

It's like they always say: "There's a sinusoid for that!"  (Well, maybe not always...)  After way too much geekiness with a spreadsheet I settled on something like this:

One "special effect" I was interested in implementing was a tapering before and after the brightest point (which indicates the actual time on the clock).  A number of false starts and bad ideas later I ended up with something like this:

But not before having too much fun with the Mac's Grapher (which I now know I am nowhere near smart enough to actually use...):

Using the NeoPixel ring-12 to represent hours and the ring-24 to represent minutes was OK, but I wanted a little something extra (feature creep alert!) for seconds.  It had to be different from both the hours and the minutes representation and still be (relatively) obvious.  Enter the white chasing taper.  A white dot makes the round of the ring-12 each second and is "chased" by a few more tapering-intensity white dots.  All that doesn't disturb (too much) the ring-12's hour display and its own tapering.