The parametric plot shows the transformation of the polar coordinate lines under the Möbius transform . The point is the image of 0, and is the image if . Transformation of the complex plane (in polar coordinates) under a Möbius transform can be observed by dragging the two points.
The code for computing the parameterization is from R. E. Maeder, Computer Science with Mathematica, Oxford: Cambridge University Press, 2000.
Wolfram Demonstrations Project
Published: March 7 2011