Sierpinski carpet twisted into the third dimension

A very familiar fractal, the Sierpinski carpet is based on a square divided into nine subsquares with the centre cut out. The result, of course, is flat. The video shows what happens if we also twist the squares along the edges. The fractal keeps the same dimension, but changes in appearance quite dramatically before returning to its original shape as it flattens out. Rendered in Persistence of Vision, like all my stuff.