The Gosper island tiles the plane, so I'm curious if a nontrivial elliptic? function exists which would have a 'period gosper-island' instead of a period parallelogram. In this case, I'm using 'trivial' to denote a function that's got the right kind of lattice, but the Gosper island is overkill and unnecessary -- for example the derivative of the equianharmonic case: $d\wp(z;0,1)/dz$ (last image).