The Weird Inner World of the 3D Fractal

This post is about one of the really cool things that happens when maths I don’t understand and technologies I don’t understand get together to make something awesome. Let us begin:

A typical fractal, made using the Mandelbrot set.


A fractal is a conceptual object that reveals further details about its shape ad infinitum, upon ever-closer inspection of it’s fabric. Think of the trunk of a tree sprouting branches, which in turn split off into smaller branches, which themselves yield twigs etc and you won’t go far wrong. In fact, fractals typically look like this thing to the right.

These infinitely complex shapes are ‘created’ by instructing graphics software to render the result of a simple mathematics formula. Until now, the result has been a 2D image – there’s no depth, shadow, perspective, or light sourcing. It is a truly abstract mathematical shape.

But since your home computer became powerful enough to do proper image rendering stuff, home hobbyists have begun to innovate on these formulae. For the first time, three dimensional fractals are able to be created with relative ease.

I can’t go into the maths, because you know, I’m not a total geek, but I do want to show you how beautiful some of these shapes are. Let’s run through some examples:


This is what you get by multiplying phi and theta by two.


More like a classic fractal with 0.5*pi to theta and 1*pi to phi.


This time multiplying angle phi by two, but not theta.




But we’re still looking at these things from outside. The really cool bit is when you start to zoom in. So let’s look at some of the high quality renders from the archives of Daniel White at his highly eclectic Skytopia, where I first learned of this phenomenon.

Make sure you click around on some of these thumbnails, yeah?!

If you’re anything like me, you’d be pretty excited at the idea of being able to create both beauty and complexity from something as simple as a few lines of code, and to then be able to explore your creation from every angle.

Then again, if you’re anything like me, you’d feel a bit frustrated that you’ll probably never be able to make something that awesome yourself. So let’s marvel at the wonder of Daniel’s creation as he takes us deep ‘Into the Heart of the Mandelbulb’.

Your comments, please!

Into the Heart of the Mandelbulb

Published by

Tom Saunter

I like to think about the media, technology, pop-culture & the future. When not blogging, I tweet @freedimensional & work @MediaComUK. Feel free to visit my Personal Bio to learn more about me.