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