I've been fascinated by tessellations in general for a very long time, so I was very interested to find the book "Origami Tessellations" by Eric Gjerde. There are some truly stunning things in the book, and some truly stunning tessellations out there in the world -- made from a single square or hexagonal sheet of paper. Just take a look at the origami tessellations group on Flickr to see what's possible.
This project is called "water bomb" and it's in the beginner section of the book. It was relatively straightforward and (unlike many tessellation projects which start with 32x32 or denser grids) only required an 8x8 grid to do the basic pattern. If you look at the right on the first photo above, you can see where I made an error with the initial creases -- there's one errant crease in the middle of one of the squares.
Brownie first wondered why I was putting this thing on her bed -- then she decided to make off with it and eat it (she has a thing about paper).