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The Structure of Recursion: Mandelbrot Superset

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Uploaded
Jan 22, 2017 | 11:35 AM EST
File Info
3200 x 3200 px
PNG
5.6 mb
Tags
fractal
julia
mandelbrot
superset

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Author Comments

Please FULLVIEW - it's 3200x3200, and a lot of subtle detail is lost at normal size.

Okay, so initially, this just looks like I took a mandelbrot and applied filters or something to it in ultrafractal. That's no what's going on, here - this comes from a custom program, and is the result of pure math.

Every point on a mandelbrot set has a corresponding julia set. Each julia set is shaped a little like that point on the julia set. If you look at a picture of the entire julia, though, it looks nothing like the mandelbrot set itself.

But the cool thing is, if you make a picture of a julia set for every point on the mandelbrot set, and then take the average colour of the pixels, you don't get static or noise. You get this image. Just like the mandelbrot contains the set of all julias, the julia contains a hidden image of the mandelbrot set!

And more. The normal mandelbrot doesn't look so cloudy, after all.

It's not *just* the mandelbrot set that you can do this with. If it's an escape time fractal, you can do it. I have some really low-quality renders of the Burning Ship Fractal's equivalent, and some other ones for other formulas. Nothing that looks as nice as this, though.