Newton's method for finding roots of zⁿ = 1 partitions the complex plane into basins of attraction — regions where iteration converges to each of the n roots. The boundaries between basins are fractal, exhibiting self-similarity at every scale. This Newton fractal arises because near the boundary, tiny changes in starting position radically alter which root is found — a hallmark of sensitive dependence. The damping parameter λ controls step size: λ=1 is classic Newton, other values reveal different fractal geometries.