Wada property: every boundary point touches all basins simultaneously
Click to zoom in at any point
Newton's method z ← z - p(z)/p'(z) converges to different roots depending on starting point.
For p(z) = zⁿ - 1 (roots are nth roots of unity), the basin boundaries are fractal — every
boundary point borders ALL n basins simultaneously (Wada property). Smooth coloring uses
iteration count for continuous gradients. Higher degree → more intricate fractal structure.
Click to zoom in on the fractal boundary.