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 z3-z and the other having a fixed critical point: z3+az2 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.