Doing the Amazing Circle trick on this one will result in a nearly identical image, with a bigger triangle in the center and a thinner circular figure on the outside.

While playing around with the AC-trick and trying to wrap my brain around what was actually happening to the images, I started considering that it should be possible to make a design that stays the same when applying the method. Since it basically comes down to flipping the image inside out you would need an image that has 'polar symmetry', meaning that if you take a line from a the center of the image to the edge, it has to form a palindrome. The basic geometry of this line shouldn't change if you reverse it. The simplest example of a geometric shape that has this property is a circle.
Doing some more thinking and experimenting I realized that the procedure is reversible: if you apply the trick to an image a second time, you will end up back where you started. This means that all you need to do is combine an image with the Amazing Circle of that same image! The result will have the original image in the center and the amazing circle as a ring around it.
This method has the advantage that you don't have to consider the 'polar symmetry' when making a design: any image will work. The only thing you have to think about is the size. I didn't, and obviously there's a difference between the 'before' and 'after' picture when you look at the size of the triangle and it's circle. It would require some more experimenting to end up with a triangle the right size (or, more precisely: an triangle with a sufficiently large white border to create a sufficiently large white center hole to accommodate the original triangle...). Maybe I'll do that some other time....