Polynomial mating: 1/6th and 5/14th

Polynomial mating is a mathematical procedure to create a dynamical system on the sphere, from two others of a special type. Here we show the procedure applied to the degree two polynomials whose parameter lie at the end of Mandelbrot’s set external rays 1/6th and 5/14th. The final dynamical system is a Lattès map. Instead of tracing the Julia sets, we drew the equator (everything is shown sideways: the equator is a vertical line) and how it deforms when the procedure is performed. The deformed curve tends to a sphere (surface) filling curve that is naturally associated to the Lattes map, as proved by Shishikura and Milnor. See ~cheritat/MatMovies/ for more details and more videos.