Brain fart....those blocks/layout has a name.
Wait...it will come to me.

It's not a Gordian Knot...but

I think the sample dunster posted was definitely pieced.
Endless Knot blocks? Is this it?
http://tlc.howstuffworks.com/home/tr...uilt-block.htm
And then you rotate them and connect the blocks.

Now, you want it very, very thin ....like 1/4" thin.
Piecing would be as much of a chore as applique with that width. And you would have all those extra seams.
So either way - quilter's choice. ;-)

How big/small are you planning on making the blocks?