About

This mini-course introduces shader programming as a tool for mathematical illustration and exploration. Shaders are programs that run in parallel on the GPU, making them exceptionally fast for visualization tasks. We’ll learn to write code that “reads like mathematics” using Shadertoy, a beginner-friendly web-based platform that handles all the low-level programming complexities.

We’ll progress from 2D foundations (fractals, tilings, simulations) to 3D rendering via raymarching. Along the way, we will implement classic examples like the Mandelbrot set, hyperbolic tessellations, the wave equation and implicit surface renderers.

No prior experience with shaders or GLSL is required—only a strong foundation in undergraduate mathematics and willingness to put in some time with code through daily homework exercises. Here are some examples of things we will make: