Nebelmesser's Playground
Computational Sublime
4D Stereo Viewer
A 4D viewer. Open the live page
or the local 4d/viewer.html.
A tesseract is two ordinary cubes sitting at W = −1 and W = +1, with matching corners joined by edges that run only along W. The viewer rotates that object in four dimensions, projects it down to 3D, and draws the result. Blue is the negative-W cube, red is the positive-W cube. Edges that cross W interpolate from one color to the other.
The camera then looks at that 3D picture — either as a single view or as a stereo pair, so the 4D shape can be seen with depth. Dolls and filled cubes are translucent so the W-axis (and the other copy) stays visible in stereo.
Inspiration
Stereo
The bar at the top picks the layout:
- Mono — one camera, full window.
- Cross-eyed (default) — two images, swapped: right eye on the left, left eye on the right. Cross your eyes until they fuse.
- Parallel — left eye on the left image, right eye on the right. Look through the screen as if into the distance.
Stereo strength is the eye separation. The convergence plane sits on the object, so changing the slider should not make the object slide sideways.
Rotation
4D rotations happen in a plane spanned by two axes. The viewer exposes the usual six: XY, XZ, YZ in ordinary 3-space, and XW, YW, ZW into the fourth axis.
| Input | Plane |
|---|---|
| Drag, or one finger | XZ · YZ (3D orbit; W is held still) |
| Shift + drag, two-finger pan, or scroll | XW · YW |
| Shift + scroll, pinch, or trackpad pinch | ZW |
On a phone, Tilt rotates (in the menu) maps device motion onto a plane:
- Off — ignore the sensors.
- 3D (around W) — tilt orbits XZ and YZ, same as a one-finger drag.
- 4D (XW · YW) — default; tilt turns the object through W.
- ZW plane — tilt is a single ZW rotation.
Invert tilt flips the sense. While a finger is down, tilt is locked so the two inputs do not fight. iOS asks for motion permission on the first tap.
Menu
The hamburger opens the settings (always open on a wide desktop):
- Object — tesseract (cube extruded in W) or matryoshka (mesh extruded in W).
- Size — how large the object is in the frame.
- Stereo strength — eye separation (hidden in effect in Mono).
- Perspective — 4D projection distance. Smaller values exaggerate how much W stretches or shrinks the copies; larger values flatten the projection toward an orthographic look.
- Fill opacity — density of the translucent W± copies.
- Fill W± — translucent caps at W = −1 and W = +1 (cubes or dolls).
- Cage — (mesh objects) a thinned wireframe of the 3D surface at both ends.
- W-axis slices — extra copies at even W values between −1 and +1. Slice count is 2–16. The tesseract draws those as wire cubes (blue→red); the matryoshka draws nested translucent dolls with the painted texture.
The tesseract still draws W-edges between matching cube corners. The doll does not: the two translucent copies and stereo parallax are enough to read W.
Axes
The HUD at the bottom is the same four axes after the current 4D rotation: X red, Y green, Z blue, W yellow. An axis that points nearly at the camera becomes a circle instead of an arrow (solid if it points toward you, dashed if it points away).
License
MIT. Made by Nebelmesser.