After reading the comments yesterday, I e-mailed John and asked if he would like to contribute a few words of explication. He replied:
I first became aware of Costa's Minimal Surface when it was mentioned in a book I was reading by Shing-Tung Yau, a past winner of the Fields medal [an international prize for outstanding discoveries in mathematics]. I didn’t understand much of the book. My family give me these tomes to read knowing they’ll keep me quiet for a long time. However, I did know enough to know that his mention of ‘a new embedded surface’ sounded like subject matter for me. This set me on a long journey trying to understand what was happening to this stretching of a torus about three puncture holes. At first glance, the description of what was happening seemed simple enough, though the math was way above my head. I spent the next twelve months or more mentally pulling, pushing, and twisting this doughnut until finally I was able to construct a 3D drawing on my Mac. I gave it some artistic interpretation. I had to. Costa threw the puncture holes out to infinity and infinity tends to use up a lot of costly material and is difficult to get out of the studio door. Anyway, it’s now just about done. Let’s see what my family give me to read this coming Christmas.