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Visualizing Complex Numbers Using GLSL – Harley Turan

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Intrigued by this series of tweets by Keenan Crane (and this exploration by Varun Vachhar), I spent a recent Sunday morning dusting off high school memories of complex numbers in order to write some pretty shaders. Keenan’s tweet showed a few formulas visualized in 2D space, and I was immediately faced with a couple of questions: Hopefully this post helps break down what’s going on here (or at least to the best of my understanding), and how we can use what we learn to play with and visualize complex numbers. GLSL, or the OpenGL Shading Language, is a graphics programming language that can be used to program visual effects. Shaders are both incredibly versatile and also conceptually simple — you write a set of instructions, and those instructions are run for every pixel on the screen. The result of those instructions tells the pixel what color it should display as. Whilst conceptually simple, shaders can be really complex to work with. Instead of thinking “I want to make the 62nd pixel

Visualizing Complex Numbers Using GLSL – Harley Turan ← Harley Turan • April 2022 Visualizing Complex Numbers Using GLSL Intrigued by this series of tweets by Keenan Crane (and this exploration by Varun Vachhar ), I spent a recent Sunday morning dusting off high school memories of complex numbers in order to write some pretty shaders. Keenan’s tweet showed a few formulas visualized in 2D space, and I was immediately faced with a couple of questions: What does any of this mean? How do I make art using it? Hopefully this post helps break down what’s going on here (or at least to the best of my u

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