Reality flows continuously, but computers measure time in frames. A simulation jumps: move everything a tiny step forward, recompute the forces, repeat ten, a hundred, a million times. Physics engines in games do this 30–120 times per second; weather models do it for the whole atmosphere in chunks of kilometers.
One step of a projectile
- Forces: gravity pulls down (−9.81 m/s²); drag pushes against motion.
- Velocity: v → v + a · dt — velocity changes by acceleration times the step size.
- Position: x → x + v · dt — position moves by the new velocity.
- Repeat until the projectile lands. That’s the whole engine.
Here’s the honest secret: the step size dt is a modeling assumption too. Big steps are fast and slightly wrong; tiny steps are accurate and expensive. In the lab you’ll compare a 30-frame simulation with a 120-frame one and see the gap yourself.
Every simulation you’ll ever meet — climate models, stock markets, game physics — makes this trade-off between fidelity and cost. Knowing it exists is the difference between using a simulation and trusting one.