Algebraic Starscapes

Algebraic Starscapes is a series of prints made with Edmund Harriss and Kate Stange during the Illustrating Mathematics semester at ICERM. They were shown at Gaukurinn, a cultural venue in Reykjavík, in 2020.

Each print draws the roots of a family of integer polynomials. Fix a shape of polynomial — $ax^2 + bx + c$, say, or $ax^3 + bx + c$ — let the coefficients run over the integers, and plot every complex root that comes back. Twelve such families were shown, and the patterns they make are not the ones you would guess from the algebra.

Two posters hung with the prints. One explained the images from a standing start, beginning with a number that gives two when you square it and subtract itself. The other set out the recipe in full, precisely enough for a mathematician to reproduce any of the twelve.