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

Get Aeon straight
to your inbox
Join our newsletter Sign up
Follow us on
Facebook
Like

‘Thought-provoking, eclectic, open-minded and user friendly.

Aeon is like no other site on the internet.’

Larry D, UK, Friend of Aeon

‘Aeon is always providing great, thought-provoking content, and it would be a crime for me to not donate to a service that I use daily.’

Jarry A, Canada, Friend of Aeon

‘I believe it’s increasingly important to support accessible scholarship and aspirational ideas.

Thinking people can no longer afford to be alone.’

Christine T, USA, Friend of Aeon

‘Aeon is my favourite online magazine.

I have found no other place that so regularly provides interesting, clear and informative articles across academic disciplines on topics that matter.’

Dr Robert J. Hartman, University of Gothenburg

‘Aeon, for me, continues to be one of the best places to spend a quiet afternoon, in the company of some of the most brilliant minds around.’

Shivam C, India, Friend of Aeon

Aeon is a registered charity committed to the spread of knowledge. Our mission is to create a sanctuary online for serious thinking.
But we can’t do it without you.

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

Essay/
History of Science
Behold: science as seeing

One astronomer’s dimpled pie is another’s cratered moon. How can our mind’s eye learn to see the new and unexpected?

Gene Tracy

Essay/
Neuroscience
The cerebral mystique

Neuroscience gives us invaluable, wondrous knowledge about the brain – including an awareness of its limitations

Alan Jasanoff