The is a set of chaotic solutions to the Lorenz system, defined by three coupled non-linear equations:

\frac{\delta x}{\delta t} = a (y - x)
\frac{\delta y}{\delta t} = x (b - z) - y
\frac{\delta z}{\delta t} = xy - c z

Enable mouse control:

On the right, you can see an implementation of the Lorenz attractor in WebGL using .

Note that the equations above are dynamic. You can click on the constants a, b, or c and change their values to radically change the appearance of the attractor.

The code that I used to create this was modified from , which contains a basic implementation in 140 bytes. I modified it to use a WebGL particle system, and dynamically respond to updates of the constants. I also added in a controllable camera, so that you can click and drag on the rendered output to change your viewpoint (although the scrolling is a little wonky - sorry about that!).

Here's the code I ended up with to make this Idyll component: