This project displays two three-dimensional fractals constructed in a way similar to the Menger sponge and the Plus fractal. A cube is cut twice across each of its order 4 symmetry axes to yield 27 smaller cubes. Imagine painting these cubes in black and white according to a checkerboard, i.e. in such a way that no neighbouring cubes have the same colour. Then, discard either the black or the white cubes, and iterate the process on the remaining cubes. Depending on which cubes are discarded, one obtain two distinct three-dimensional fractals, which we'll call Checkerboard I and Checkerboard II.

Here are some stereographic views, as well as a stereographic video of a rotating Checkerboard I fractal. Look at the left image with your right eye and vice versa to see them in three dimensions.

Here is a cut across one of the order 4 symmetry axes.