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How to compute the dimension of a fractal
Find out what it means for a shape to have fractional dimension.
Content about “ fractal
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Article
The Abel Prize 2022: Dennis Sullivan
This year's Abel Prize goes to the "true virtuoso" Dennis Sullivan.
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Fantastic fractals
Escaping the tyranny of the straight line.
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What is the Mandelbrot set?
This article gives a short but thorough introduction to that fabled beast of mathematics: the Mandelbrot set.
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Maths in a minute: Local connectivity
How crinkly is crinkly?
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The Tower of Hanoi: Where maths meets psychology
Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi. Yet, the puzzle holds fascination in both fields.
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Exotic spheres, or why 4-dimensional space is a crazy place
For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like?
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Wiring up brains
The human brain faces a
difficult trade-off. On the one hand it needs to be complex to ensure high performance, and on the other it needs to minimise "wiring cost" — the sum of the length of all the connections —
because communication over distance takes a lot of energy. It's a problem well-known to computer scientists. And it seems that market driven human invention and natural selection have come up with similar solutions.
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Eat, drink and be merry: making it go down well
This article is part of a series of two articles exploring two ways in which mathematics comes into food, and especially into food safety and health. In this article we will take a dive into the rather smelly business of digesting food, and how a crazy application of chaos theory shows the best way to digest a medicinal drug.
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Fractal music
Fractals are a treat for your eyes, but what about your ears? Dmitry Kormann, a composer/keyboardist from São Paulo, Brazil, explains how he integrates fractal-like patterns in the very structure of his music, to obtain beautiful results.
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Non-Euclidean geometry and Indra's pearls
If you've ever redecorated a bathroom, you'll know that there are only so many ways in which you can tile a flat plane. But once you move into the curved world of hyperbolic geometry, possibilities become endless and the most amazing fractal structures ensue. Caroline Series and David Wright give a short introduction to the maths behind their beautiful images.
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Unveiling the Mandelbrot set
You've probably seen pictures of the famed Mandelbrot set and its mysterious cousins, the Julia sets. In this article Robert L. Devaney explores the maths behind these beauties and shows that they're loaded with mathematical meaning.