Ha.nnes.dev

Plotting roots of monic Littlewood polynomials (and monic polynomials with coefficients of 1 and other numbers).

Explanation

Littlewood polynomials are polynomials with coefficients of either 1 or -1. Monic polynomials have the first coefficient as 1. This script plots the roots of every N-th degree monic Littlewood polynomial on the complex plane.

Usage

The two main functions are find_roots(polynomial_order, other_no) and render(image_name, points, plot_centre, plot_scale, image_size) where the points argument is the output of the first function.

Examples

An example of the density of the roots of every 20th degree monic Littlewood polynomial.

A high resolution render of the same image.

Zooming in on a section.

A 1920x1080 desktop background image.

A rotated version of the same image for phone wallpapers.

An animation of changing a parameter from -1 to 1. (Full video here)