#you've got all those in depth zooms of the mandelbrot where there's a mini mandelbrot surrounded by like twenty arms
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It really fucks me up that the boundary of the Mandelbrot set has Hausdorff dimension 2
Like, a space filling curve? Sure, that LOOKS like it converges to dimension 2. The limit of a generalized Koch snowflake as the angle approaches zero? Sure, it "closes up" in an obvious way.
But the Mandelbrot? It's so sparse! It's got big ol gaps!
#Math stuff#tesserants#my understanding is that it gets Squigglier on average as your zoom level increases so i guess that makes sense#you've got all those in depth zooms of the mandelbrot where there's a mini mandelbrot surrounded by like twenty arms#so#sure#but it still feels wrong!
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