This project displays pictures of the iterations of a 3d Hilbert curve, a curve filling the three-dimensional volume of a cube. See this project for 2d Hilbert curves.

All the images below are stereographic. Look at the left images with your right eye and vice versa to see the curves in 3d.

The curve is constructed in an iterative way. We start with the following path, which is contained in a cube (not shown on the picture).

The cube is then cut in two along each axis, yielding 8 twice smaller cubes. If we rotate/mirror these elementary cubes suitably, and draw the original path in each of them, we obtain a more complicated path, the second iteration of the 3d Hilbert curve:

The process is repeated again and again, and the true 3d Hilbert curve is the limiting curve, as the number of iterations tend to infinity.

Some more views of the 4th iteration