The Starry Night — Iterates of Tan(z)

“The Starry Night” is a “mathematical Van Gogh”, giving us a glimpse of a nebular cluster which has been generated by mathematical, as opposed to natural, forces. The study of this pattern falls under the iteration theory of Fatou and Julia, which examines discrete dynamical systems on the Riemann Sphere Ĉ with a dynamic given by a non-linear holomorphic or merornorphic mapping from Ω ⊂ Ĉ to Ĉ (see [1–3])…