These are sort of Photoshop creations... and sort of not.
-WARNING-
math stuff ahead
I've always felt that the best way to get a good intuition for topological surfaces was to generate illustrations of them by hand
(1). The final illustrations I end up with are the surfaces sliced into sections so you can also see what is happening inside. The idea is that the sections could be sewn together to make the complete surface
(2).
Well, after taking all that time to actually create the illustrations, I had never taken the additional step of trying to bring the same pieces together... until now.
I took a number of illustrations I had drawn over the last few years and, in Photoshop, displayed both the original spread out sections and the sections brought close together.
So rather than take up room on the page displaying the new versions of the illustrations that I made in Photoshop, I'll just link to them for anyone who is interested.
(1) My drawings start out with contour (fold curve) diagrams, then producing level sets (which are associated with the slices), and followed by generating the actual surface sections between the level sets. I can then go back over the illustration and look for critical points to make sure that the surface I've drawn is actually the surface I had intended to draw... all of which is beyond what I would guess anyone would really care to know about.
(2) This technique is a little different than the one used by my professor (example from here) which looked at surface "bands" for each of the level sets. I like seeing the full surface personally.
