Here is a minimal surface based on the Weierstrass-Enneper representation . Written explicitly as a function from the complex number z to 3-space it is .
It is based on my old tanh surface, but has a wilder style. It gets helped by the fact that my triangulation in the picture is pretty jagged. On one hand it has two flat ends, but also a infinite number of catenoid openings (only two shown here).
I call it Håkan’s surface, since I came up with it on my dear husband’s birthday. Happy birthday, Håkan!