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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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Ecology and environmental sciences
GPS tracking reveals stunning insights into the patterns of migratory birds
6 minutes
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Human rights and justice
Can providing humanitarian aid be illegal? A troubling case from the US-Mexico border
17 minutes
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Space exploration
The rarely told story of the fruit flies, primates and canines that preceded us in space
12 minutes
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Film and visual culture
A lush animated opus evokes the frenzied pace of modern life
4 minutes
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Family life
The precious family keepsakes that hold meaning for generations
10 minutes
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Neuroscience
This intricate map of a fruit fly brain could signal a revolution in neuroscience
2 minutes
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Archaeology
What did the first people who entered Tutankhamun’s tomb see?
5 minutes
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Information and communication
Coverage of the ‘balloon boy’ hoax forms a withering indictment of for-profit news
17 minutes
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Childhood and adolescence
Marmar is living through a devastating war – but she’d rather tell you about her new dress
8 minutes