Blaschke product · unit disk automorphism
Each factor slides the unit disk onto itself without tearing it: points inside stay inside, the boundary circle stays the boundary. With three poles arranged symmetrically the circle is wrapped three times around itself, and the dense web of images of straight rays and circles is what draws the pattern. The same maps describe lossless filters in signal processing, where |B| = 1 on the unit circle means no energy is gained or lost.
right-click · learn & record
