Nitpicky, but calling something R^3 outside of an academic context when '3D' suffices leaves me feeling oversold and underdelivered. This is 3-dimensional, and no further info is added with R^3 while only making it slightly less approachable.
R^3 contains R^2 and R, but I can't change the view to just 2D or 1D, so why call it R^3?
tldr: the original idea came to me while studying homeomorphisms of various topological spaces embedded in R^3, thus the name.
My original goal was to visualize homeomorphisms in R^3 and verify closed forms for some of them. I'm used to calling it R^3 because there are many 3-dimensional spaces (C^3, {0,1}^3, etc) and there are many embeddings into R^3 that are homeomorphic (e.g. D^2 is 'z==A and x^2 + y^2 < 1' for every A). So the context is a bit academic. Visualizing a continuous deformation ended up being pretty cool -- I ended up "inventing" a traversal in a metric space that is very similar to BFS, but works for metric spaces, by repeatedly selecting a subset of it fitting in a progressively bigger open ball. You might know a concept pretty similar to this as filtration.
Might make sense to use two coordinate systems for source and target?