Chaos Bouncing Balls Lab
Hundreds of balls, 2D collisions, and chaos intuition from tiny perturbations.
why tiny deltas become huge differences 🖖
This system is deterministic, but still chaotic: a microscopic seed delta in initial velocity can produce radically different trajectories after many collisions. Divergence growth is linked to repeated nonlinear interactions and impact ordering. The equations are fixed; predictability horizon is what shrinks.
two worlds racing to disagree 🖖
This lab is really a race between two almost-identical universes. You launch a second run with a microscopic velocity nudge (seedDelta) and watch a divergence meter climb while the two ball clouds still look overlapping. The takeaway: let them run long enough and the number always wins — determinism does not guarantee predictability. Restitution e sets how much impact energy survives each collision.
round balls are chaos machines 🖖
The chaos is not in the balls but in their shape. When two round balls collide, a hair's-width difference in the contact point throws the rebound angles apart, because a convex surface spreads nearby trajectories like a diverging lens. Mathematician Yakov Sinai proved this in 1970: a flat box with a single circular obstacle (the Sinai billiard) is rigorously chaotic, while a plain rectangular box is not. Curvature, not force, manufactures unpredictability.
Example problems
- Ideal Elastic - Ideal elastic regime: energy largely preserved, with persistent bouncing and mixing.
- Damped - Damped regime: drag and inelastic walls dissipate kinetic energy over time.
- Chaotic Cloud - Dense cloud: frequent collisions amplify microscopic differences into macroscopic divergence.
- Near-Identical Twins - Twin-run demo: almost identical starts diverge visibly, illustrating chaos intuition.