Hypercube Tesseract Simulator (2D)

4D Rotation

Rotation speed 0.60 rad/s

Rotation Plane

Display

4D camera distance (w) 3.20

Rotating in the XW plane.

Live Readout

Vertices

Edges

Rotation angle

0°

Plane

How it works

A tesseract's 16 vertices sit at every combination of (±1, ±1, ±1, ±1) in true four-dimensional space. An edge connects two vertices whenever they differ in exactly one coordinate — that rule always produces 32 edges, the same count a cube's 3D analogue has doubled.

Each frame every vertex is multiplied by a real 4D rotation matrix that turns two of the four axes into each other (XW, YW or ZW) while leaving the rest fixed — this is not a visual trick, it is the literal higher-dimensional analogue of spinning a 2D square inside 3D space.

To draw the result on a flat canvas, the rotated 4D point is perspective-projected: divide x, y and z by (camera distance − w), the same trick a 3D-to-2D camera uses but with the fourth coordinate standing in for depth. Vertices are grouped by their original w-sign into an "inner" and "outer" cube — as the shape rotates, those two cubes appear to grow through one another, which is exactly what a real tesseract looks like when it turns in 4D.

Rotation speed sets how fast the 4D angle advances.
The plane buttons choose which pair of axes (X-W, Y-W or Z-W) the rotation mixes.
4D camera distance controls how strong the w→3D perspective divide is — closer distances exaggerate the inner/outer size difference.

Inner cube (w < 0 at rest) Outer cube (w > 0 at rest) Bridging edge between cubes