# Index of /~cheritat/MatMovies/Magic

# Siegel disk | Magic formula applied to Siegel disk

One is the degree two polynomial P1 having a fixed point with multiplier exp(2 pi i theta) where theta is the golden mean. The other is the polynomial P2 obtained from the first by applying Douady's magic formula: consider the external angle alpha of the parameter for P1. Let beta = alpha/4 + 1/2. The external ray of the Mandelbrot set with angle beta lands on a real parameter. This is P2.
The mating of P1 and P2 is a degree two rational map with a Siegel disk and a critical orbit relation.