It's just a matter of subtracting the two functions, taking the absolute value, and putting that number through a color ramp. If you want to see the result in 3D you can subtract the functions and throw that into a 3D graph plotter. Building a 3d surface plotter would be the hard part, but they already exist, eg plug "abs(y/(x^2+y^2) - (x+1)/(x^2+y^2))" in here:

https://c3d.libretexts.org/CalcPlot3D/index.htmlT

This viewer also has a "2d" mode that produces a colored 2D plot.

trouble is, i'm more engineer than mathematician, so while i appreciate that this is an entirely solvable problem, assembling it from scratch would likely mean many errors, and less fun

the 3d plot is nice but not what i would call "spatialised", since it's still a flat render, and I'm exactly thinking about the meshing of the thing. i am familiar with delaunay and marching cube strategies, at least enough to get a machine to hook them up to a spatial plotter