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TESSERACT: Visualizing the 4th Dimension (ℝ⁴ to ℝ³)
The Architecture of the Unseen
Human perception is limited to three dimensions, but mathematics allows us to step beyond those boundaries. I developed the Zelvior Tesseract Interface to visualize the theoretical "Hypercube"—a 4-dimensional shape that defies standard physical intuition.
How it Works: While a standard cube has 8 vertices and 12 edges, a Tesseract consists of 16 vertices, 32 edges, and 24 square faces. This interface uses Stereographic Projection to map these 4D coordinates onto your 3D screen. By manipulating the "W-axis" (the fourth dimension), you can witness the famous "inside-out folding" motion that occurs as the shape rotates through 4D space.
Key Technical Features:
Real-time Telemetry: A live data feed tracking rotation angles (in radians and degrees) across all six 4D planes (XY, XZ, XW, YZ, YW, ZW).
Bivector Rotation Control: Unlike 3D objects that rotate around an axis, this engine allows you to control rotations within 4D bivector planes.
Customizable Physics: Adjust the "Stereo Radius" to change how the 4th dimension is projected, or toggle "W-Depth Coloring" to see which parts of the cube are "closer" to the 4D eye.
Research-Grade HUD: Designed with a futuristic terminal aesthetic, featuring FPS tracking and ω (angular velocity) magnitude charts.
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