There is a channel on youtube called 3blue1brown where Grant Sanderson does 
exceptional math videos. I have heard interest in quaternions expressed in the 
J community so I will put in some links that provide visual explanations of 
quaternions and how to visualize their actions across 4 dimensions.

Initial video introducing quaternions: 
https://www.youtube.com/watch?v=d4EgbgTm0Bg

Short video introducing an interactive tool to investigate quaternion 
behaviour: https://www.youtube.com/watch?v=zjMuIxRvygQ

Site containing the interactive videos https://eater.net/quaternions  (yes 
these videos are interactive and can be manipulated in real time!)

Enjoy

Cheers, bob
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