I was talking with my father last night and he mentioned that he thought he had discovered a new optical illusion. He was about to boil an egg and had put it into a saucepan with a small amount of water in it. Then he just happened to spin the egg so it rotated in the pan and was immediately struck by the fact that the egg looked as if it was changing shape rather than rotating. It was as if the shell was flexible and something inside it was pressing outwards at different places to give an impression of rotation. He said he spent quite a time playing around with the egg to confirm that the the illusion of changing shape was quite persistent.
Now, I don't think my father is senile (yet) so, this evening, I set out to try to investigate this 'illusion' for myself. Waiting till Zoe had gone to bed (I didn't want her to think I have gone senile), I took one fresh egg, one hard-boiled egg and saucepan and had a little play with them. I found that with the fresh egg I definitely could 'see' it as changing shape although I had to look carefully to do so. However, I do not think this is due to some sort of 'optical illusion' but is rather a consequence of the way fresh eggs rotate: they do not rotate smoothly. The liquid inside must 'slosh about' and cause the angular momentum (rotation speed) to vary in a pulsating sort of way, and this is what gives the impression of 'something inside pushing out'. This seems to be confirmed by the behaviour of the hard-boiled egg which rotated fast and smoothly and did not give any impression of changing shape.
Incidentally there are quite a lot of basic science articles on spinning eggs available on the web: do a search on Google.