Strange Immersion Skin Art

a tattoo.

As it turns out, this is not exactly the same surface. The monkey saddle from (IV) has been moved all the way down to the bottom (VII), skipping a few twists and turns along the way. The move was needed in order to make a single picture that was both visually and mathematically interesting. (My friend would never have settled for a tattoo that she knew was topologically equivalent to a disk!) What this means is that there are in fact two such immersions of the torus in 3-space. An interesting question would be: can you deform one into the other?

design/photo © 1994 Cassidy Curtis