# Polynomial matings on the Riemann sphere

## Newton maps as matings

### z^3-z | z^3 + az^2

Among the rational maps, there is a particular class that implement Newton's root-finding algorithm on a polynomial. These maps are called*Newton maps*for brevity. In the class of degree 3 Newton maps, there is a subset that can be described as matings of two degree 3 polynomials, one of them being z

^{3}-z and the other having a fixed critical point: z

^{3}+az

^{2}for some complex number a that depends on the situation. This movie illustrates a particular example, which belongs to a

*Mandelbrain*. The second polynomial in the mating can be found in the copy of the Mandelbrot set that is attached at the main tip of the main hyperbolic component.

- The movie above (mp4, 2.7MB)
- Flat version (mov, 2.1MB)
- Variant where the rabbit is a single component (wmv, 1.6MB)