Well, I have absolutely no idea what you wanted, but you got me playing around with tilings, so here's an interesting one:
I'd like to name this The Holy Pattern, because it's literally just a bunch of holes connected to each other, leaving holes in between. Out of the 17 possible wallpapers, this is the pattern "p4".
You can make this pattern with various different hole sizes and different sized gaps in between. That's not the clever bit.
Each of those patterns nicely tiles a plane. That's not the clever bit either.
The clever bit is how you can construct the pattern. Holes in various colours, then placed at the proper slots? Or just pick the smallest rectangle that repeats? Well, you could do either. However, it's possible to construct the pattern from a single piece containing a single hole. I'll use a different sized pattern with different eye-assaulting colours to demonstrate.
Start with a single hole not surrounded by a single colour:
Mark the centres of the adjacent holes. Using one of those points as a pivot, make four rotated copies of the initial piece. Notice how this creates additional pivot points.
Then you can either keep pivoting, OR you can notice that the resulting piece is rotationally symmetric (well, we constructed it by rotating stuff around the centre, so, yeah..), and start to pivot using that piece. This is so much nicer, since we can just copy and paste:
And so on, ad infinitum.
It's probably a good idea to add some thickness to the walls, and you can even add colour to the some of the holes by choosing a different shaped starting piece:
Repeating the whole process with this piece will result in a pattern that's hopefully at least a little less.. jarring than the ones above.
If this wasn't at all what you were looking for, my apologies. At least I had fun :-)