Doubly Periodic Surfaces
Complete, embedded doubly periodic minimal have always anular ends which come, after rotating the surface, in top and bottom ones. All top ends and all bottom ends are necessarily parallel, but the top and bottom ends either make an angle or they don't. Strangely, this dichotomy seems to persists when a surface is deformed.
Parallel Ends with Wei type nodal limits
Parallel Ends with Scherk components
Numerical Examples (existence unproven)