Another fractal, and one with a satisfying story behind it. Newton's method is the standard way to hunt down where an equation equals zero: guess, see how far off you are, adjust, repeat. It usually works.
Here every pixel on the screen is used as a starting guess for the same equation, which has several answers. Run the method and each guess eventually homes in on one of them. Colour each pixel by which answer it found, and the screen divides into territories. The startling part is the borders: however far you zoom in, two neighbouring pixels can end up at different answers, so the boundaries never resolve into a clean line. They are fractal all the way down.
degree sets how many answers there are and so how many territories. The one to experiment with is relaxation: instead of taking the full correction each step it takes a fraction or an excess of it, which makes the method overshoot and spiral, twisting the territories into pinwheels.