I laughed when I saw the pattern because it reminded me of a free-arm quilting pattern known as a stipple.  Stipple can be large or small, depending on the scale to fit the item being quilted.  The Hilbert Curve is known as a filler curve; so appropriate for quilting, don’t you think?

Talking this over with my husband, he then mentioned the Sierpinski Triangle.  Here’s the logic to the Sierpinski Triangle in quilting terms:

Start with a 9-patch comprised of only two fabrics, white and a patterned fabric.  That is the base to work from.  Now, consider a 9-block wall-hanging.  Using the same pattern as used in the single, 9-patch block, wherever you used the patterned fabric, in the 9-block wall hanging, you would use that 9-patch block.  Let’s say your original block had this:

White – White – Pattern

White – Pattern – White

Pattern – White – White

The blocks would be laid out like this:

White – White – 9-patch

White – 9-patch – White

9-patch – White – White

Get it?

Expand that to a larger quilt, comprised of 9 wall hangings, and you’d see:

White – White – Wall-hanging

White – Wall-hanging – White

Wall-hanging – White – White

That makes for a LOT of white, right?

Here’s the thing:  you could really use ANY 9-patch pattern, just repeat it per the Sierpinski Triangle logic and you’d have a HUGE variety of quilts that would be very cool (not to mention very simple to put together).  In the example, I used white, but you really could use ANY fabric setup, as long as you chose one of the original 9-patch fabrics to represent the location in the grid where that pattern would repeat.  

Below is an illustration I found on Wikipedia that immediately made me think quilt.  Not only did it make me think quilt, it made me think quilt using different values of the same color wherever you see red, so that it would start with a strong color in the upper right corner and fade into the white, so to speak.

Quilt it using a stipple in the form of a Hilbert Curve, and, my friends, geek your heart out over that.