Newton Fractal Basins

Newton's method z ↦ z − f(z)/f′(z) — color by root, shade by convergence speed

Click to zoom in  |  Right-click to zoom out
Polynomial
Newton iteration:
zn+1 = zn − f(z)/f′(z)

Color = which root
Brightness = speed
Fractal boundary:
dim ≈ 1.5–1.9
Julia set structure