Eryk Kopczyński

Normally when you pick cells closer to cell A than to cell B, you get a half-space. But if you are in a highly symmetric closed hyperbolic manifold, the result looks much more interesting. This manifold is constructed of 260 right-angled dodecahedra. Two dodecahedra A and B in distance 5 are chosen, and walls are put on the dodecahedra which are closer to B than to A. (Each dodecahedron is in distance 1 to 12 adjacent dodecahedra.)

A flocking simulation in hyperbolic space. The camera follows a specific bird. Other than being in non-Euclidean space, this simulation follows roughly the same rules as the classic "Boids" simulation. In an Euclidean space, all the birds would fly on parallel lines, at the same speed. However, this is hyperbolic geometry, so there are no parallel lines: birds close to the center on the flock will fly in a straight line, but ones not lucky enough to get in the center will fly in a longer, curved line, lag behind, and possibly be forced to leave the flock.