Menger Sponge (level 2)

Images are licensed under the Creative Commons Attribution-NonCommercial 4.0 International License

This is a labor-intensive, but very satisfying to fold model. Some people have managed to go as far as level 3 but even level 2 was quite challenging. About halfway through this model, I got interested more in other things, and it spent about half a year in partially finished state before I continued.

Business cards 5×9 cm in size were used to fold this piece. Placed side by side, they would cover an area of over 15 m², the size of a large room. Due to large size (almost half a meter edge length), this model has to be stored on the floor, causing inconvenience. On the other hand, it seems children enjoy pushing it around and hiding toys in its numerous holes. Since it’s a modular design, it’s relatively easy to repair any damage as long as you still have some business cards from the original set lying around as spare parts (cards from a different set will usually differ at least a little in color).

One of the images shows three Menger Sponges side by side: level 0, level 1 and level 2. This illustrates nicely how each higher level sponge can be built from repeated instances of a sponge one level lower and how the complexity (and thus the number of modules required) quickly grows with each iteration of this fractal. The sponges are made of 12, 192, and 3456 units, respectively.

One of the images shows the model in January 2023, 9.5 years after it was folded, decorated with Christmas lights.