One of my art activities is crocheting hyperbolic surfaces. They are inspired by mathematical ideas and by nature as it may occur in sea life. I love smooth curved lines, and wavy surfaces. That was one very big reason which attracted me to mathematics, in particular topology.
This surface started out as a plain hyperbolic disk. At some point, rather than crocheting a single loop around the disk, I crocheted two parallel loops around the same disk, one in white and one in purple. Thus a central disk at its perimeter branches into two parallel annuli. They turned out to have more or less the same curvature, which is why they run pretty much in parallel. I made them to intersect each other, so that I could crochet the entire object in one go. This is a technical challenge, something I love to solve.
This object started out as an ovoid. I then crocheted two axes on
opposite sides of the ovoid. With each subsequent loop along these
axes around the ovoid I increased the top and bottom extensions of
For the ovoid I used a thicker plastic wire, so that it would keep its large, relatively flat shape (of varying positive curvature). For the wavy hyperbolic algae parts I used a thinner plastic wire, permitting more negative curvature.