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Aeon is a registered charity committed to the spread of knowledge and a cosmopolitan worldview.
But we can’t do it without you.

Aeon is a registered charity committed to the spread of knowledge and a cosmopolitan worldview. Our mission is to create a sanctuary online for serious thinking.

No ads, no paywall, no clickbait – just thought-provoking ideas from the world’s leading thinkers, free to all. But we can’t do it without you.

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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

Support Aeon

Ideas can change the world

Aeon is a registered charity committed to the spread of knowledge and a cosmopolitan worldview.

But we can’t do it without you.

Aeon is a registered charity committed to the spread of knowledge and a cosmopolitan worldview. Our mission is to create a sanctuary online for serious thinking.

No ads, no paywall, no clickbait – just thought-provoking ideas from the world’s leading thinkers, free to all. But we can’t do it without you.

Become a Friend for $5 a month or Make a one-off donation

Essay/Biology
The minds of plants

From the memories of flowers to the sociability of trees, the cognitive capacities of our vegetal cousins are all around us

Laura Ruggles

Essay/Earth Science
Life goes deeper

The Earth is not a solid mass of rock: its hot, dark, fractured subsurface is home to weird and wonderful life forms

Gaetan Borgonie & Maggie Lau