Donut-shaped C code that generates a 3D spinning donut

The video presents a fascinating visual demonstration where an ASCII spinning donut appears on the left side of the screen, while the corresponding C code that generates this animation is displayed on the right with syntax highlighting. This creative project was developed by Andy Sloan, whose work explores the intersection of mathematics and programming to render complex 3D objects using text-based graphics. The presentation highlights how a simple circle can be transformed into a torus, often referred to as a "Taurus" in this context, through specific geometric operations that form the basis of the visual effect. The mathematical foundation for generating these spinning donuts involves several precise steps: first creating an initial circle, then rotating it around the y-axis to form the toroidal shape. Once the 3D structure is established, rotation matrices are applied to spin the object along both the x and z axes, simulating movement in three-dimensional space before projecting the final image onto a two-dimensional screen. To add depth and realism, the code calculates surface normals for illumination purposes, determining how light interacts with different parts of the donut's geometry based on a specific light source position. A unique feature of this ASCII-based rendering is its ability to map varying levels of luminance to distinct characters, creating a textured appearance that mimics shading in traditional computer graphics. The code includes adjustable parameters such as the field of view and the distance between the viewer and the donut, allowing users to customize their perspective. Additionally, an optimized version of the code incorporates a microsecond sleep function specifically designed to aid in smooth animation timing when compiled and executed on different systems. Beyond the technical demonstration, the creator shares personal insights into their daily routine of spending at least an hour exploring topics outside their primary professional focus. This dedication to curiosity drives the production of quick videos that showcase beautiful concepts ranging from machine learning and computer science to psychology, biology, physics, history, and philosophy. The overarching goal is to share these discoveries with an audience interested in both basic and advanced subjects within STEM fields and beyond. The video serves as a bridge between abstract mathematical theory and tangible visual output, inviting viewers to explore the underlying mathematics behind such animations via Andy Sloan's blog post linked in the description. By combining rigorous geometric principles with creative coding techniques, the project illustrates how complex 3D rendering can be achieved using simple text characters. The final result is not only a visually engaging spinning donut but also an educational resource that demystifies the process of generating such graphics through code and math.