Plus Advent Calendar Door #19: Fun with fractals

Share this page

Oh, those beautiful snowflakes! They've put us in the mood for fractals, so let's celebrate some favourite shapes:

Pandora's 3D box
An amateur fractal programmer has discovered a new 3D version of the Mandelbrot set. The new creation is based on similar mathematics as the original 2D Mandelbrot set, but its infinite intricacy extends into all three dimensions, revealing fractal worlds of amazing complexity and beauty at every level of magnification.

Unveiling the Mandelbrot set
And if you're wondering what the Mandelbrot set is to start with, here's an introduction from one of the world's experts.

Modelling nature with fractals
Computer games and cinema special effects owe much of their realism to the study of fractals. This article takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.

How big is the milky way?
A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Learn how fractal dimension gives us a way of approaching the question.

Extracting beauty from chaos
Images based on Lyapunov Exponent fractals are very striking. Find out what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.

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.

Back to the Plus Advent Calendar

Read more about...
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.

  • Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!

  • How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?

  • Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.

  • PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.