It confused me a lot - I cancelled the denominators in my head too.

But then I realised they're just plotting

y/(x^2+y^2) - (x+1)/(x^2+y^2) = c

and colouring by c (i.e. a heatmap, as others have mentioned in the thread).

That's why you get a more interesting image than you'd get with y - (x + 1) = c