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Joined 1 年前
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Cake day: 2023年7月7日

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  • rustydrd@sh.itjust.workstoScience Memes@mander.xyzDimensions
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    5 天前

    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.









  • rustydrd@sh.itjust.workstoScience Memes@mander.xyzHero
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    1 个月前

    Many people I know get into it because of their idealism and desire to change the academic system for the better. They invest into this career, year after year, because it’s always one more step until they can finally use their influence to change the system from the inside.