Basin boundaries for complex root-finding — fractal structure at every scale
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Newton's method z_{n+1} = z_n − f(z_n)/f'(z_n) converges to different roots depending on starting point z₀ ∈ ℂ. Color = which root was reached; brightness = convergence speed. The basin boundaries form a Julia-like fractal — every boundary point is on the boundary of ALL basins (Fatou-Julia theorem).