Instrument 003 · does the map help?
Two particles start ε apart with the same heading. Their motion follows a deterministic rule that is known from the start. With the scatterer off, they remain close in this square billiard. Switch it on and watch their sampled paths separate. The rule still determines each path. At finite precision, however, the two starting positions can lead to different cells in the coarse read. Run both versions to compare them.