In and Outside the Torus

Today’s math-art is about a torus, and is called In and Outside the Torus. It’s created by Thomas Banchoff.

According to Prof. Banchoff,

[this] is an interior view of a cyclide of Dupin, a torus on a three-dimensional sphere in four-space projected stereographically from a point on the torus itself, leading to a third-order algebraic surface expressed as a union of circles (and four straight lines). These curves are orbits of a Hamiltonian dynamical system and the fibers over a great circle of the Hopf mapping from the three-sphere to the two-sphere

Now, if this is confusing, don’t worry. Just sit back, and enjoy the colors. On a slightly more interesting note, if you want a full mathematical explanation (if you understood the above, chances are you wouldn’t need to, and if you didn’t understand the above, chances are you wouldn’t want to either), Prof. Banchoff provided a full account of the mathematics behind the torus.

This mathematical art is IMO, awesome, as it has a very nice usage of colors. In fact, I’d rate it one of the best maths-arts I’ve seen so far. It is bold, for one. Tell me what you think of it as an art work.