2024 Joint Mathematics Meetings
Stephen J Trettel
Artists
Stephen J Trettel
Assistant Professor of Mathematics
University of San Francisco
San Francisco California, USA
Statement
When illustrating mathematics, I focus on illustrating low-dimensional geometric objects which embody both visual and mathematical beauty. My primary medium consists of 3-dimensional computer graphics, and I typically write a new program for each piece. I aim to capture each mathematical object in its natural environment, and provide a view of what it 'would really look like' were it possible to visit the abstract world that it calls home.
Artworks
Limit set in Jade
51.0 x 61.0 cm
Output of a custom program written in GLSL (graphics language on GPU)
2023
Discrete groups of symmetries of hyperbolic space leave a trace of their geometry out at infinity - as an intricate collection of points known as the *limit set*. This piece depicts one such limit set - a fractal living in the 3-sphere arising from a group of symmetries of hyperbolic 4-space. To compute the image, a program was written to raytrace points of the fractal using the escape-time algorithm of Jos Leys, stereographically projected into $\mathbb{R}^3$. Then to render, a custom path-tracer was written to simulate a "jade-like" material: each pixel is colored by simulating 50,000 individual photons, each of which scatters inside of the material on a variant of a random walk.