Newton's method attractors reveal fractal structure in the complex plane
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Click to explore — zoom in near boundaries to see fractal structure
Newton's method for finding polynomial roots partitions the complex plane into basins of attraction — one per root. Near the roots the boundaries are smooth, but riddled near triple/quadruple junctions: any ε-ball near a boundary point intersects all three basins, creating perfect fractal interleaving (Hausdorff dimension = 2).