Danielle Amethyst Brake

Assistant Professor of Mathematics
University of Wisconsin-Eau Claire
Eau Claire, Wisconsin, USA

I am a visualizing and computational mathematician. My primary love is programming in the field of Numerical Algebraic Geometry. I became fascinated with 3D printing after a surprising revelation that a program I was writing could be used to produce models. I've continued to enhance my software, so I can make 2D line art, and visualize arbitrary nonlinear projections of n-dimensional algebraic curves and surfaces, as well as arbitrary functions evaluated over those same objects. I find mathematics, particularly computational algebraic geometry, fascinating and am passionate about visualizing it.

78 paths to decompose a sphere
78 paths to decompose a sphere
10 x 8 cm
Digital art

In numerical cellular decomposition, a computer program repeatedly solves an ODE. Decomposition of the sphere takes a total of 78 paths. Most of them are entirely over the complex numbers, with few ending at real points on the sphere itself. Here we see those few paths, with their jaggedness coming from numerical predicting and correcting as the homotopy paths are walked. Consider the tremendous amount of computation that happens in our daily lives: how much of it is hidden from us, the focus on result and outcome, and the bliss of ignorance to process. Such are the paths to this sphere.