Unlike normal, I was able to deliver the square version of the descending pentagons quickly. There was no math to figure out. although there was one interesting choice that I looked into. The choice was to place the 45 triangles to be touching the previous square rather than the corner square. I guess it's simply a preference about complexity. I like both. The first version is a simple analogue of the descending pentagons--actually it was the original doodle on my boogie board. I find the boogie board is a great exploratory tool because of it's impermanence. Somehow it helps me focus on process rather than product. The version of the boogie board I have doesn't save any of your work and there is no erase so you are stuck with any mistakes unless you erase the entire drawing. So I am tasked with focusing on the internalizing any thing that I do that I think is important. Perhaps this is a bit of a throw back to all the time I spent with chalk and blackboards. Regardle…
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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 wall (colour), wall (blue), 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.