Brane is also known as membrane in current string-theory physics. It speaks to one of several possible time/space 4-D surfaces interacting among others. Please recall string theory still has a lot of problems regarding dark matter and it is just a theory, subject to revision by men and women who think Einstein was a good place for beginners to get started.
This part of the site was intended to help collect references to spacial reality as we the writers know it.
Why yes, you’re right, I am reminded of that Escher artwork where the hands with pencils recursively draw one another. Funny you should mention it.