Newton Fractal
Newton’s method finds roots fast — but which root it finds depends wildly on where you start. Colour every point of the complex plane by the root of zⁿ − 1 it converges to and the boundaries between the basins shatter into infinitely fine fractal filigree, where a nudge of the starting point lands you on a different root entirely. Pick the degree of the polynomial, adjust the iteration budget, and darken by convergence speed to expose the structure.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Newton’s method iterates z ← z − f(z)/f′(z); for zⁿ = 1 there are n roots evenly spaced on the unit circle.
- The basin boundaries are a Julia set — near them, arbitrarily close starting points converge to different roots.
- Brightness encodes how many iterations convergence took, revealing the fractal’s onion layers.
- Runs 100% in your browser — simulations are computed locally on your device.
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