Controls
Interaction Guide
- Hover and drag to control rotation
- Mouse movement affects rotation speed
- Automatic smooth transitions
About
This visualization demonstrates a 4D hypercube (tesseract) projected into 2D space. The colors represent different vertices, and the gradients show the connections between them.
Built with SVG and JavaScript. Interface designed with Tailwind CSS.
The Mathematics Behind the Hypercube
1. 4D Rotation
We rotate the hypercube in 4D space using rotation matrices in multiple planes (xy, xz, xw, yz, yw, zw), allowing us to see different aspects of its structure.
2. Stereographic Projection
We project from 4D to 3D using the method w' = w/(w-d), where d is the distance to the projection point, creating a 3D shadow of the 4D object.
3. Perspective Projection
Finally, we project the 3D shadow onto a 2D screen using standard perspective projection, maintaining depth cues through size and opacity.