Hyperbolic Billiards

Game

Geometry

Table

Table

Table

Fractal

Each press follows every line of the web through 10 more corner hits. The lines are where the rule breaks down; the gaps between them are islands where balls circle forever.

Model of the plane

Same table, same shot, drawn three ways. Watch straight lines become arcs.

View

Unfolded: instead of the ball bouncing, the table flips over the wall. The path becomes one straight line through a tiling.

Shot