Littlewood

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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

<xml.dom.minidom.Attr object at 0x7f43ff797a10> — An example of the density of the roots of every 20th degree monic Littlewood polynomial.

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

<xml.dom.minidom.Attr object at 0x7f43ff7978c0> — A high resolution render of the same image.

A high resolution render of the same image.

<xml.dom.minidom.Attr object at 0x7f43ff797700> — Zooming in on a section.

Zooming in on a section.

<xml.dom.minidom.Attr object at 0x7f43ff797540> — A 1920x1080 desktop background image.

A 1920x1080 desktop background image.

<xml.dom.minidom.Attr object at 0x7f43ff797230> — A rotated version of the same image for phone wallpapers.

A rotated version of the same image for phone wallpapers.

<xml.dom.minidom.Attr object at 0x7f43ff796f20> — An animation of changing a parameter from -1 to 1.

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