Okay, thanks for the explanation:
Here is what I researched so far:
I started out by letting a favico generator generate an image out of a big spiral picture:
Then I created my own, based on a simple start and then cycling around with large flat lines on the north, south, west and east side
Then I generated a favico out of this:
This gave me the hint that these triangles coming from the center feel a bit strange, but also somehow help giving the feeling of roundness on the corners ...
Anyway thats what I got so far in terms of "round" spirals; edgy spirals are quite a lot easier with white space inbetween, but even there it would be interesting to see weather or not one can give the spiraly illusion without having white space ...