Hyperbolic space
Geodesic planes, flat horospheres, and a round ball with different intrinsic tilings.
cargo run --release -p hypertrace-examples --bin hyperbolicBrowser viewer
Optional. Requires WebGPU; starts only when requested.
Native requirements and instructions
Technical details
Drag to look; Tab locks the mouse. WASD moves; Space/C moves up/down; Q/E rolls. Scroll zooms; R resets. The viewer pauses when hidden or outside the page’s visible area. Open viewer separately.
What to observe
Compare the fivefold patterns on the planes with the square and hexagonal patterns on the horospheres. Find the small tiled ball between the surfaces.
- A geodesic plane has negative intrinsic curvature. A horosphere has a flat intrinsic metric, even though both are surfaces in the same hyperbolic space.
- The ball’s surface has positive intrinsic curvature. Its dodecahedral pattern uses the same selector as balls in the Euclidean and spherical examples.
- Move toward the patterns: equal camera movements cover equal physical distances, while half-space coordinate scales change with height.
Screenshots
Click an image to open its full-resolution PNG.
Settings · Render source
Camera and settings · Render source
Original video
Watch the original Hypertrace walkthrough. Historical footage of the earlier renderer; its scenes and controls differ from this version.
The original approach was inspired by Game of Life on the Lobachevsky plane. See the original project article.