I'm an artist and mathematician. My art attempts to produce a nexus between abstract mathematical beauty and the natural world to produce a satisfying aesthetic experience.
I've been examining Kuen's surface for a very long time.The red shape is Kuen's surface as seen from above, looking down the z axis. Kuen's surface is well known since it has constant negative Gaussian curvature except on sets of measure 0. This surface is virtually never seen from above, which is intriguing and beautiful.
The shapes are are nodes of a twisted torus knot. In producing the model, surface normals were reversed to maintain color interest and mathematical harmony. A torus knot is a knot that lies on the surface of an unknotted torus in R3. A long period of tinkering led to this final image.