Using Map Object along with Filter All Layers and a lot of setting up, one can make an object appear to fold along an angle somewhere between 0 and 90 degrees:

In the above, I took a rectangle, set up a lot of guides, rotated the rectangle about 26 degrees, cut off various selections of the rectangle, used Map Object and Filter All Layers to animate those selections, combined them with what was left of the original rectangle after cutting, rotated everything back minus 26 degrees to essentially arrive at the above animation.
One could even make extended animations, like for instance, after each piece folds over, fold part of that piece back. Naturally, the more folding involved, the more complex the animation, the more setup work will be involved.
This was an experiment just to see what it would take to make this sort of animation type using Gimp. Thanks for checking it out.

P.S.: I purposefully left out the shading/lighting part of the folding animation. Adding it in would add to the realism of the effect, but again, this was the result of an experiment to see what it took to create this effect.