Newton's Method Root Finder Screensaver
The Newton's Method Root Finder screensaver runs a real live Newton's method, drawing the tangent line at each guess as it converges on a root of a random polynomial. It is free, runs in your browser, and ESC exits.
How the Newton's Method Root Finder screensaver works
The saver plots a real random polynomial curve, then starts Newton's method from a random initial guess.
At each step, the real tangent line at the current guess is drawn, and the next guess is exactly where that tangent line crosses zero.
Each new guess is usually far closer to a true root than the last, exactly the fast real convergence Newton's method is known for.
Once the guess settles on a real root to high precision, it holds briefly, then a fresh random polynomial and starting guess begin.
A worked example
A guess that starts far from any root can swing wildly on the first tangent step, then rapidly snap closer and closer to the true root within just a handful of real iterations.
Settings & tips
- Accent recolours the current tangent line.
- This is a real, unmodified Newton's method implementation.
- A fresh random polynomial begins automatically once a root converges.
Frequently asked questions
- Is this real Newton's method?
- Yes — a real, correct implementation, with every tangent line drawn exactly where the algorithm actually places it.
- Can it ever fail to converge?
- Yes — real Newton's method can diverge or cycle for some starting guesses; the saver simply restarts fresh when that happens.
- Is a key needed?
- No — it is a pure local computation.
- Is it free?
- Yes — free, no download, in your browser.