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littlewood-matlab

Plotting the roots of monic Littlewood polynomials in MATLAB.

Language: MATLAB
Source code: GitHub

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.

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

A high resolution render of the same image.

A high resolution render of the same image.

Zooming in on a section.

Zooming in on a section.

A 1920x1080 desktop background image.

A 1920x1080 desktop background image.

A rotated version of the same image for phone wallpapers.

A rotated version of the same image for phone wallpapers.

An animation of changing a parameter from -1 to 1.

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