For those curious what practical usage this might have, there is a control technique that uses the position of roots to determine how a system will behave as the feedback gain is changed https://en.wikipedia.org/wiki/Root_locus

Or basically, how loud can you crank an amplifier before you hear feedback (and how does it behave with different levels of feedback)

This is GREAT! Reminds me of the http://explorabl.es/ project. The library it links to is very cool as well - http://jsxgraph.uni-bayreuth.de/wp/

Cool, really enjoyable to play around with. This made me notice a cute (probably trivial) phenomenon that I haven't seen before. If you take x^n+...+1 and move one of the roots to 1 (equivalently, divide x^(n+1)-1 by (x-z) where z is some nth root of unity), then the resulting polynomial's coefficients seem to be the nth roots of unity.

By the way, it doesn't seem to prevent you from entering a degree higher than 7 if you enter the number manually even though it gives off a warning. Not sure if this is intentional.

I wanted to keep the UI from getting too busy, which is why I limited the degree to 7. But if somebody really wants to play with higher-degree polynomials, I'm not going to stop them!

Could you open source the code? I think this tool would be really helpful for one of my professors in explaining gain margin for feedback systems.

Hi, yes, it's open source. My web site's github repo is at https://github.com/duetosymmetry/web-site/tree/customization . The JS for controlling the web toy is at https://github.com/duetosymmetry/web-site/blob/customization... . This relies on a modified version of Polynomial.js which I will hopefully get accepted upstream, but for now it's just on my fork at https://github.com/duetosymmetry/Polynomial.js/tree/Aberth (though this is also behind my local repo).

This is unreasonably enjoyable. Would also make a great musical toy...

Very cool to see one graph moving when changing the other graph. I must find a way to make cools fractals with that concept

If you restrict the possible coefficients, and limit the maximum degree, you get interesting fractal patterns: https://johncarlosbaez.wordpress.com/2011/12/11/the-beauty-o...