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#Noisevember! I revisited the Littlewood polynomial sound from day 2 of Noisevember. I thought to investigate a different sort of polynomial. Here, instead of polynomials with coefficients all ±1, the polynomials have coefficient ±1/(n+1) on the x^n term. As before, all roots of all such 15th degree polynomials are considered. (I really should create a gallery of these root plots so we can easily compare them.) Along the way, I realized I was making an error with the way I created "random" stereo that introduced a bunch of unneeded noise. So that's something! I'll have to go back and replace the Littlewood polynomial sound. soundcloud.com/matthew-m-conro…

Here's a plot of the roots (essentially the spectrogram of the sound).

#noise #sound #audio #math #maths #mathematics #polynomials #roots

A plot of all roots of all 15th degree polynomials with terms ±1/(n+1)x^n. The roots are tiny blue dots on a white background. They form a ring around the origin at the center of the plot, with something like fractal filigree around the outside of the ring. The roots are symmetric: each quadrant is identical.

15th degree polynomial roots

A track made from the roots of all 15th degree polynomials with terms ±1/(n+1)x^n.
SoundCloud
#audio #noise #math #maths #sound #mathematics #roots #noisevember #polynomials

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