Interactive Lab / The Newton Fractal

Escape-Time Discovered 1879

The Newton Fractal

zn+1=znp(zn)p(zn),p(z)=z31z_{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.

Rendering…