Rob Halliday, Andrew Lee
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Anton Lukyanenko and Platon Lukyanenko
Mathematica and POV-Ray
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In hyperbolic space, things look smaller as they get closer to the XY plane, so a ball traveling straight will look like it's changing size and moving along a curved line. Collisions are defined infinitesimally by Euclidean physics, but these have to be adjusted for non-infinitesimal objects. In the simulation, the balls can't bounce out of the green sphere. The video below shows the same balls from a different view, where hyperbolic space fits entirely within a single sphere.