I haven't done anything like this quilt. But this idea came to mind when I saw the picture. Seems like I've read about it somewhere....
Stack up several large squares of different fabrics.
Cut a curvy line through all layers.
Put the top slice from the first fabric on the bottom on the stack.
Cut another curvy line through the whole stack and repeat the process of moving one slice.
Repeat as desired.
Of course, the squares get smaller as the pieces are sewn back together. I have NO idea how to figure out what starting sizes result in what completed sizes! Guess it might take some experimenting!
Maybe this won't work, but I can't figure out why not.
Sue