Algebraic Starscapes

The beautiful patterns that appear when algebraic numbers are plotted with sizes determined by complexity (such as functions of the discriminant), revealing geometric structure.

2019-09-01

This project with Kate Stange and Steve Trettel began at the ICERM Illustrating Mathematics programme (Fall 2019) when Kate Stange put up the image of the quadratics:

Image of quadratic algebraic numbers on the complex plane, sized by discriminant

There is SAGE code to work with here.

We are currently working on shaders to render the images faster, this turns the diophantine approximation from results into practical tool.

Projects

Algebraic Number Starscapes

The first paper on algebraic starscapes, starting from pictures to solving polynomials, through geometry to research results. One goal was to show how short the path from high school accessible math to the cutting edge could be.

Algebraic Starscapes — Gaukurinn Exhibition

Exhibition of a series of Algebraic Starscapes prints at Gaukurinn, Reykjavik, Iceland.

Related

Illustrating Mathematics

Strengthening and making visible the role mathematical illustration has always played in mathematical discovery.