For a differentiable complex-valued function \(f\) with multiple zeros, Newton’s method will partition the complex plane into regions, one for each zero, each region consisting of all initial seeds \(z_0\) for which Newton’s method converges to that zero. The boundary separating these regions tends to have fractal-like qualities, so we refer to them as Newton fractals.
Fractals generated using oriont.net/newtonfractal/ by Elijah Tarr.