Thanks Daniel,
amazing!!!
One little comment though, in your definition, you probably forgot to connect the 3rd item from list item to explode
Probably one or two ‘undos’ too much before saving! 
(otherwise one of the borders stayed at the same level as the main surface)
Riemann.gh (14.8 KB)
Thanks Aris,
Yes - that surface does behave a little differently at the borders than the one shown in the original image.
So I modelled and relaxed the Karcher saddle tower surface:
but then I noticed it’s not the surface we’re looking for, since it doesn’t let you walk from one level to another.
The periodic surface I was thinking of, which is locally like Riemann’s surface is similar to the one above, but shifted half a bay, so the tunnels connect diagonally:
You can see the difference between the 2 surfaces above if you take a vertically moving section
AMAZEMENT OVERLOAD!!! 
EDIT: Can I ask you something if I’m not getting tiring?
In this part of your definition you used transform. I would expect you to just anchor them like in the side edges. Is this a way to keep a smooth curvature when stacking the meshes?
It’s a topic close to my heart.
I did a project when I was a student on some related surfaces, which I’ve returned to several times:
The surface in the right hand side of the animation in my last post can be seen as a row of vortices/helicoids of alternating direction.
Oh, and you’re quite right that in this case the same thing could have been achieved probably more easily by just anchoring the sides in the Y direction. I didn’t think of that!
There are some other cases where you want to relax surfaces while keeping the boundaries periodic, but not on a plane, but here the surfaces are mirrored about the plane, so either will work.
Thank you, Daniel and Aris. They are amazing, definitely overload for me, but I learn a lot 
Hi,
yeah pretty amazing stuff here 
Maybe the attached double helix surface gets your started…
DoubleHelixSpiral.3dm (119.5 KB)
Jess
Hi Jess, thanks for your file. But I think your file is Rhino 6, I only have Rhino 5.
Thank you, Jess 
Hey Daniel, Im currently working on a studio project at uni and am very intrigued by your explorations as your research very closely relates to my studies including Paul Virilio. Im just getting into grasshopper etc and I was wondering how you were able to create those different iterations as shown in " Rheotomic surface / flowline relationship" video. Ive tried following adding the missing components to the [Rheotomic_Surfaces.gh] example but how could i create the iterations you have shown in “Rheotomic surface / flowline relationship”?
Kind Regards,
greatly appreciate your work !
