#minibrots

The small copies of the Mandelbrot set are appealing because they have all sorts of intricate patterns around them. Each one is slightly different, and they get more complex as you zoom to higher magnifications. Diving for minibrots is one of those addictive things that can easily consume way too many hours of any given day.

Once you've found a good minibrot, then what? You can put some kind of coloring on it and call it done. You can use the intrinsic symmetry of the patterns around it to make a really lovely elaborate mandala design, and it will always have the familiar mandelbrot shape at the exact center of it. But what if you don't want that? What if you want the radial symmetry, but with a nice clean empty space in the center?

So here we have the Angel of Flimsy Comic-Book Logic.

This is a photograph of part of the ceiling in the Charlottenburg Palace.

When I first saw this picture, a number of years ago now, I immediately thought it looked a lot like the kinds of patterns you get around minibrots. Which made me wonder what Baroque-era designers might have done if they'd had access to actual fractal geometry, and then made me wonder how close I could get to this same effect.

If I start with something like this

and add a lot of gold filigree and whatnot

Pretty close. It's a lot of work, though. I've been tinkering with this version for at least a week (for more hours per day than I like to admit to), and according to my records I have several dozen older and less successful attempts dating back to 2018.

The minibrot at the center of the symmetry is too small to see, at this magnification, but it only takes a little bit of a zoom for it to show.