↓ ↓ ↓ Instructions ↓ ↓ ↓
The set of all 2D Julia set images form a 4D volume. This page lets you browse this 4D volume using interactive orthogonal 2D planes. In 4 dimensions there are 6 (4 choose 2) orthogonal 2D planes, so there are 6 views. The image centers track the same coordinate in 4D and update together.
Drag any of the images to pan the center of view and see all the other planes update. Click the "Big!" button to maximize the current plane for a closer look. The URL stores the 4D volume position, and can be shared like a bookmark.
In the top-left view you initially see the Mandelbrot set on the AB plane. In the bottom right you see a Julia set on the CD plane. By dragging just the Mandelbrot image you'll see the various Julia sets in the bottom right. The interactions between other pairs of planes are less intuitive but still interesting.
The axes on each image are colour coded so that each major axis in 4D is consistently coloured on each image. For instance the green axis which you see above is always the same axis from the 4D Juliaset volume.
You need a browser with WebGL support to view this page properly. If it's not working for you then you can try to diagnose the problem here: http://get.webgl.org/
In the meantime here's a screenshot so you can see what you're missing:
Written by Paul Richards (@pauldoo)
Code is here: http://github.com/pauldoo/scratch/tree/master/JuliaMPR