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You know the weirdest shit about fractals is that if the fractal is space filling (you repeated the pattern at all scales for infinity and end up filling a 2d area with lines somehow than that fractal exists between the integers definitions of dimensions). A 1d simple line fractal pattern can through the bullshit magic of math have a dimensionality of 1.65 or whatever, it is weird shit.

I am sure I got something wayyyy wrong about this lol, but whatever.

Eh, there’s probably worse ways to go insane.

Fun fact, the Mandelbrot set is a 2-dimensional set (because it’s defined in the complex plane). However, its boundary line is a fractal, which can be understood as having a non-integer dimension (i.e., between 1, the topological dimension of a line, and 2, the dimension of a plane). There are multiple ways to define fractal dimensions such as the Hausdorff dimension. For example, the Sierpinski triangle has a Hausdorff dimension of 1.58. But the Mandelbrot set is special here, too, as it seems to have a Hausdorff dimension of 2, meaning that its boundary is so curly that it fills “a plane’s worth of space” despite its line-like topology.

Silly, the Mandelbrot set is just 2D. Payback’s a bitch, motherfucker.