Recently, while reading about the Möbius transformation, I found this picture:
As written on the Wikipedia page, this represents an hyperbolic Möbius transformation. Does this remind you of anything?
Personally, when I look at the blue lines in this picture, I think equipotential lines of a charge dipole:
The red lines in the first picture also seem to correspond to the field lines in the second one. I just learned about the existence of Möbius transformations, so unfortunately I'm not sure what the red and blue lines are supposed to represent exactly.
I know that there is a connection between 2D electrostatics and complex numbers: after all, complex number are somehow similar to (although more general than) 2D vectors.
However, now I'm wondering: what is the exact connection, if it exists, between Möbius transformations and equipotential lines in 2D electrostatics?
