• rustydrd@sh.itjust.works
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    4 days ago

    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.

  • Sotuanduso@lemm.ee
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    5 days ago

    He spins you around for fun, and puts you back when he’s done, but off by a hundredth of a degree. Depending on how strict your interpretation is, you either no longer exist in the same 3D universe except at that single point of intersection, or you will drift off from it the further you move from your current location.

  • aberrate_junior_beatnik@lemmy.world
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    5 days ago

    I forget where I heard this but someone mentioned that a 4-dimensional being could mirror you. Doesn’t sound so bad until you realize your amino acids & stuff would all be the opposite chirality, which means you could no longer process food.