Newton's method for zⁿ − 1 = 0 on the complex plane
Newton's method applied to zⁿ = 1 converges to one of n roots, each assigned a color. The boundary between attraction basins is a fractal (Julia set) with Hausdorff dimension 2. No matter how far you zoom in, the fractal boundary remains infinitely intricate — a consequence of the chaotic dynamics of complex iteration.