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

Essay/History of Science
Does science need mavericks?

Staid and conformist, science risks losing its creative spark. Does it need more mavericks, or are they part of the problem?

Adrian Currie

Essay/Cosmology
Universe in a bubble

Maybe we don’t have to speculate about what life is like inside a bubble. It might be the only cosmic reality we know

J Richard Gott