I would like to use Blender to model minimal surfaces or soap films that are bound by a closed loop of edges. Something like below. If it could be mathematically accurate even better. I know Rhino has the ability to do this and also Sketch has a plugin too. Can blender do this? Ultimately I would like to be able to control tension and pressure parameters to adjust the shape of the resultant surface. Is there a way to do this inside blender?
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You can get something similar with a cloth sim. You will have to play around with the settings quite a bit.
In this example the white frame is a different object and does not influence the cloth ( I just put it there to “frame” the cloth/soap). The cloth/soap object uses a vertex group for pinning.
Here is the file (3.3), to see the result hit play for the simulation to run.
Soap.blend (221.5 KB)
Edit:
This is fun! with a positive pressure value you can blow bubbles! 
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Hey that is brilliant!!! I stupidly didn’t think of the cloth simulator as having that ability. I will give it a go with the forms I am trying to reproduce. Thanks so much @DNorman
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Yes cloth sims are great, there are many more possibiliteis like adding force feilds (wind etc).
Have fun!