Welcome to the world of Origami Fractals! Technically speaking, a fractal cannot be properly represented by an Origami design, but with enough effort they can come close.
Many different shapes can be used to create a fractal, but this site will be focussed on cubes. The most recognised cubic fractal is the Menger Sponge:
Image from fg.tribes.cc: Menger Sponge from Level 0 to Level 3
A great deal of study has gone into the classic Menger Sponge, as discovered by Karl Menger. But if you apply a different generator, you can get variants of the Menger Sponge:
Original Images, click to view correct size: Variant 12 Menger Sponge from Level 0 to Level 3
I have so far found no name for this variant, so I will refer to it as the "Variant 12 Menger Sponge", as it has 12 smaller holes surrounding each large hole, instead of eight smaller holes surrounding each large hole in the classic Menger Sponge.
Many different shapes can be used to create a fractal, but this site will be focussed on cubes. The most recognised cubic fractal is the Menger Sponge:
Image from fg.tribes.cc: Menger Sponge from Level 0 to Level 3
A great deal of study has gone into the classic Menger Sponge, as discovered by Karl Menger. But if you apply a different generator, you can get variants of the Menger Sponge:
Original Images, click to view correct size: Variant 12 Menger Sponge from Level 0 to Level 3
I have so far found no name for this variant, so I will refer to it as the "Variant 12 Menger Sponge", as it has 12 smaller holes surrounding each large hole, instead of eight smaller holes surrounding each large hole in the classic Menger Sponge.