Fractal charm: space-filling curves

3 minutes

Mesmerising fractals and space-filling curves give a window into infinity

First discovered by the Italian mathematician Giuseppe Peano in 1890, a space-filling curve can theoretically expand endlessly without its path ever crossing itself to fill an infinite space. In a computer display, space-filling curves are limited by the number of pixels on a screen, but watching these fractal constructions extend isn’t just hypnotic – it’s also a helpful (if somewhat imperfect) demonstration of the enigmatic concept of infinity. To learn more about the mathematics of space-filling curves, watch Hilbert’s Curve, and the Usefulness of Infinite Results in a Finite World, also by 3Blue1Brown.

Video by 3Blue1Brown

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