Mathematicians--
The first article referenced below mentions Iverson and APL in early pages, but 
the graphic notation is definitely more complex than either APL or J.  I am not 
competent to judge whether some of the operations they discuss are amenble to J 
implementation, or would be worthwhile.

For those interested in notation per se, two additional references discuss 
notations for quantum interactions pictorially, and in Quon, which requires 
three dimensions to notate its operations.
--Art

ATL:
http://people.csail.mit.edu/lamanda/assets/documents/LiuPOPL2022.pdf 
<http://people.csail.mit.edu/lamanda/assets/documents/LiuPOPL2022.pdf>

Mathematical picture language:
https://mathpicture.fas.harvard.edu <https://mathpicture.fas.harvard.edu/>

Quon:
https://www.pnas.org/content/pnas/115/1/81.full.pdf 
<https://www.pnas.org/content/pnas/115/1/81.full.pdf>

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