These are instructions for making a certain origami tessellation pattern, pictured above. Though this kind of origami is often called a "tessellation", this is not really the right word.
This pattern has the symmetry group of the Wallpaper pattern p4m also called *442. You can find out more about Wallpaper patterns at Xah's Wall paper patterns page.
You can gradually accentuate the creases to flatten the paper like this:
Take a single "unit" of this pattern, such as the following:
The image can be repeated:
This repetition of the image was made using a java program I'm writing which I will add a link to when it's finished.
But we can also actually repeat the origami itself. In the next picture, the same pattern is folded twice in the same piece of paper:
The smallest possible "unit" which is repeated over and over by only using translations, not reflections or rotations, looks like this
To make it fold as shown in the following pictures:
Let me know if you would like instructions in words. Whether they appear will depend on whether there's any demand.
If you would like to see even more units being folded, click the following image.