You have to reload this page to see the animation ...perhaps I should put it on a bit of a repeat. It took a surprising amount of high school math to unravel how to make this. I guess I could have been content with just eyeballing it but that seems to take all the challenge away plus it makes it more difficult to augment later. Perhaps I should have used a better tool than Excel: maybe Geometer's Sketchpad. Next time. Perhaps I'll put up the square version of this pattern when I get the time.
Essentially, it's a snazzy version of starting with a pentagon and using the sides midpoints to make a slightly smaller pentagon and descending forever (or in this case 12 levels?). The snazziness is was the time consuming part. Computing the lighter bands took a bit of effort--more of a stamina thing rather than a difficult thing.
I was going to try to get this into last month but alas February only has 28 days this year.
here is a toned down copy that works for wallpaper
and wall (sepia).
I was a bit lazy using a tool to crop it so it's in pdf rather than svg...but my MacBook pro accepts it as my desktop background so I didn't pursue it.