We are excited to share our latest tutorial exploring the fascinating intersection of art and math: **Torus Knot Patterns**.

Our primary aim was to guide users on how to create a Torus knot using the powerful **Scene Nodes workspace in Cinema 4D** and how to add custom patterns to make the resulting structure visually striking. Torus knots are a special type of mathematical knot defined by a pair of integers P and Q that describe how the knot wraps around the surface of a torus (a donut shape). They have real-world applications in fields like molecular chemistry and topology.

The video starts by showing you how to build a **fully procedural Torus** using `nside` nodes for the ring (longitude curve) and the pipe (meridian curve), connected via a `sweep line` node. The core challenge then involves simplifying the complex mathematical formula that defines a Torus knot into a practical node setup. We use key parameters (theta, P, and Q) along with arithmetic and trigonometry nodes to calculate the final 3D coordinates (X T, Y T, Z T) of the knot.

Using this procedural approach, we successfully generated the raw shape of the Torus knot. By changing the P and Q values, we demonstrated the creation of the simplest knot type, the **trefoil knot**.

To take the visual results a step further, we explored applying **decorative transformations** to the knot patterns. Drawing inspiration from research on generating artistic variations of knot structures, we built a custom node setup based on these concepts to transform the pattern, showcasing how mathematics and node logic can result in a beautiful scene.

It is truly amazing how combining a bit of math and Scene Nodes in C4D can produce such intricate and beautiful abstract results.

If you want to see the detailed step-by-step process of setting up the mathematical formulas, defining the curves, and applying decorative transformations using Scene Nodes in C4D, **please click** [**here**](https://www.youtube.com/watch?v=Tebcnlp8gHA)**!**

Creating Mathematical Torus Knots Procedurally in Cinema 4D Scene Nodes