SETTING IN

I finally, through trial and error and math figured out how to get an acceptable vortex.  There are things that I would change, but I made 4 samples before I got to this one and I'm pretty much ready to move on.
Once it was finished, I had to figure out how to fit the circular block into a square background.  I finally came up with this idea.
Freezer paper and an unthreaded sewing machine. I'm sorry that the photos are rotated.  I fixed them, but they revert to the original orientation anyway.

I pinned the block onto a piece of freezer paper and stitched a quarter of an inch seam around the edge.  This will be the seam line. 

Then, sew 1/4" inside that seam line to get the area to cut out

This is the circle cut out leaving the seam allowance.
Take the background fabric fold into quarters to find the center.  I found that cutting around the removed round piece of freezer paper is easier, so I ironed that onto the background and cut around that to make the opening. 

Fold the background piece into quarters and press. this will give 4 creases.  Then fold the block into quarters and place pins at each edge.  you should have 4. Align the pins with the creases and pin each section between.  Stitch a 1/4 " seam around the edge and

Ta Da!!  A Perfect Fit.