Lorenz Attractor
Classroom worksheet · Interactive simulation: https://lkforge.com/tools/physics/lorenz-attractor/
Name: Date:
Learning objectives
- Describe deterministic chaos and strange attractors.
- Observe sensitive dependence on initial conditions.
- Distinguish chaotic from random behavior.
Variables to change
- Initial conditions
- System parameters
Procedure
- Run the system and watch the trajectory trace the two-lobed attractor.
- Start two trajectories from nearly identical points and watch them diverge.
- Let it run and confirm the path never exactly repeats yet stays bounded.
Observations
Describe the shape of the attractor and how quickly two close starts separate.
Questions
- What is a strange attractor?
- Is the Lorenz system random?
- What is the "butterfly effect"?
- Does the trajectory ever settle to a point or loop?
- What did Lorenz originally model with this?
Answer key (instructors)
- 1. A bounded set that a chaotic trajectory is drawn to but never repeats, with fractal structure.
- 2. No — it is deterministic; the same start gives the same path, but tiny differences grow exponentially.
- 3. Sensitive dependence on initial conditions — small changes lead to vastly different outcomes.
- 4. No — it stays bounded but never repeats, endlessly circling the two lobes unpredictably.
- 5. A simplified model of atmospheric convection (weather), which is why it launched chaos theory.
The Lorenz system is deterministic yet chaotic: trajectories are drawn to a bounded, never-repeating "strange attractor," and nearby starts diverge exponentially (the butterfly effect). It arose from weather modeling and helped found chaos theory.