I don't know the actual terminology for the specific fold, but I was wondering if it was possible to create something like it.
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Hi Please use a title that reflects the content of the question. It should be descriptive but succinct, unique and identifying, summarizing the issue so that users can at a glance understand what your post is about. Use the [edit] link below your post and avoid anything not strictly essential to the post. Remember, your title is the first thing potential visitors will see, and makes your question findable for future users. See "What is the problem with posting an image or link and asking “How do I do this?"" – Duarte Farrajota Ramos Feb 19 '23 at 00:09
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https://blender.stackexchange.com/questions/71721/how-to-make-a-curtain https://blender.stackexchange.com/questions/98315/how-to-create-a-cloth-stage-valance https://blender.stackexchange.com/questions/196739/how-can-i-get-this-curtain-to-open-and-close-realistically – Duarte Farrajota Ramos Feb 19 '23 at 00:13
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I believe it should be quite possible. What I see (translated to some blender terminology you can search this site for):
- Start with a plane that is subdivided into sufficient faces and subdivision surface modifier for smooth rendering,
- create several vertex groups each containing what will be hung from real-world hooks
- hook each group to an object or empty (Vertex(menu): Hook to new object, ctrl-h),

- select all vertex group vertices and create a new vertex group
"Pinned" (i.e. union of all subgroups).

- use the Pinned vertex group in the Cloth Shape Pin Group.

I defined the individual hook groups be be too wide in my example, but this should give you an approach. You might also want to
You might then start to Apply the Cloth modifier as the initial frame (frame 1), and recreate the cloth modifier for subsequent animation.
You might also want to adjust weight painting of the vertex groups that are hooked to the empties to adjust the quality/stiffness of how they follow the hooks (gradient). 
james_t
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