# Ha.nnes.dev

## Littlewood

Plotting the roots of monic Littlewood polynomials in MATLAB

2020-08-02

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)