Pseudosphere
Playing with constant negative curvature
The pseudosphere is the surface you get by spinning a tractrix around its asymptote. It has constant negative curvature, so every patch of it is a piece of the hyperbolic plane. Here are a few things I've been playing with on it recently.
Self Portrait
A nod to Escher's Hand with Reflecting Sphere, but with a pseudosphere for the mirror. The surface is rendered in POV-Ray as a reflective lathe of the tractrix, placed inside a 360° photo so the reflection shows the real surroundings.
The Klein Quartic on Dini's Surface
Dini's surface is a twisted cousin of the pseudosphere, and it also has constant negative curvature. That means you can map hyperbolic tilings onto it with no distortion. Here it carries the heptagonal tiling of the Klein quartic, colored the way it is in MagicTile.
Flying
My friend Stephen (red suit) and me (white) flying in the wind tunnel at iFly, with pseudospheres traced in the air around us.