I know next to nothing about the technicalities of fractal geometry, but from an award-winning site for elementary and middle school students, I’m beginning to understand self-similarity, which is central to its definition. As the ancient dictum puts it, “As above, so below,” the macrocosm mirrored in the microcosm.
As for how fractals are embodiments of mathematical formulas, another ancient saying applies: “He doesn’t have a clue.” But I’m happy to leave the particulars to the mathematicians and just enjoy the images, many of which can be seen here.
Here’s a two-minute animation of a Mandelbrot set that could go on forever.
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