Interactive Lab / The Newton Fractal

Escape-Time Discovered 1879

The Newton Fractal

zn+1=zn−p(zn)p′(zn),p(z)=z3−1z_{n+1} = z_n - \frac{p(z_n)}{p'(z_n)}, \qquad p(z) = z^3 - 1
★Cool Fact
A completely deterministic, local root-finding method — yet the global map of which root each starting point converges to is a fractal. All three basins meet at every point on their shared boundary.

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