The Rainbow Connection

For today’s post I present a teaser for a rather important realization that I made regarding the formation of toroidal helical orbitals.

If I take a long and narrow helix with a single turn and bend it twice around itself, I get a string that loops around a toroidal (donut) surface twice before touching its tail. For a long time, I had just assumed that If I made identical copies of these toroidal orbitals, I could fill a whole surface of a donut with them.

However, when I actually tried to do this, I wasn’t able to. Once I thought about it, the reason became obvious. One has to twist the helix around its central axis before bending it. That’s because each of the helices bend differently, depending on their orientation before bending.

To illustrate this phenomenon, I decided to make the bent structure with strings of all the colors of the rainbow. And this is how it looks like:

How any of this relates to the Theory of Everything, I’ll tell in another post. Today’s post was just for aesthetics.