Dror Bar-Natan's Image Gallery:Knotted Objects:

Braided Thetas

A braided Twenty
Click on the image for a sharper view.

What does this image show? That the two figures below, of embedded ribbon graphs in R3, are topologically equivalent. This is far from obvious!

A braided theta graph

How was it made? I scanned a twenty dollar bill, stretched it 50% lengthwise for easier braiding and folding, printed it, cut slits in the print (see the upper half of the image), braided it, scanned the result, and shrank it 50% lengthwise. So I didn't mutilate a real Twenty, and I never printed anything that remotely looked like a counterfeit bill. Don't call the Secret Service.

Another example:

A braided Dollar
Click on the image for a sharper view.

This one was made by Dylan Thurston following a suggestion by Curtis Moore. Action photo: Action photo of Dylan (click to enlarge).