Newton's method is a well-known root finding method in scientific computing. If it converges to a root then it is highly accurate and very fast. However, the method is only locally convergent. The boundary between two or more domains of local convergence can be very complicated. In this video we zoom onto one such boundary for a complex valued polynomial of order 3. Each shade of green represents convergence to one of the three roots. While it never fully repeats itself, the basic structure appears to be self-similar, which is why the boundary is called a fractal.
For further information see
en.wikipedia.org/wiki/Newton_fractal
Music: Bobby Richards, Two Moons, 2020