Newton's method applied to z^n − 1 produces a stunning fractal. Each point in the complex plane is colored by which root the iteration converges to, and shaded by how quickly. The boundaries between basins are fractal — they are nowhere smooth, and every boundary point is simultaneously on the boundary of all n basins (Julia-set style). The Hausdorff dimension of the boundary is strictly greater than 1. Zoom in to explore infinite self-similar complexity.