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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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Biology
Butterflies become unrecognisable landscapes when viewed under electron microscopes
4 minutes
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War and peace
Two Ukrainian boys’ summer unfolds just miles from the frontlines
22 minutes
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Nature and landscape
California’s landscapes provide endless inspiration for a woodcut printmaker
10 minutes
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Love and friendship
Never marry a man you love too much, and other views on romance in Sierra Leone
5 minutes
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Engineering
Can monumental ‘ice stupas’ help remote Himalayan villages survive?
15 minutes
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History of technology
Curious singles and tech sceptics – what ‘computer dating’ looked like in 1966
6 minutes
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Cognition and intelligence
A father forgets his child’s name for the first time in this poetic reflection on memory
4 minutes
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Animals and humans
Join seabirds as they migrate, encountering human communities along the way
13 minutes
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Stories and literature
Two variants of a Hindu myth come alive in an animated ode to Indian storytelling
14 minutes