Lorenz Attractor

This simulation integrates the Lorenz system, a simple model of convection that shows chaos. Students adjust sigma, rho and beta, set the size of the tiny start offset for the second trajectory and toggle it on or off. The blue path is the reference run and the orange path starts almost in the same place. Readouts show the separation between them, an estimate of the growth rate and the time to separate. Teachers can use it to introduce sensitive dependence on initial conditions and the butterfly effect.

• Keep the classic values and watch the blue and orange paths separate over time.
• Change Start offset to a smaller power of ten and read the Time to separate readout.
• Lower Rho below about 24 and see whether the motion stops being chaotic.
• Compare the ln(d/d0) / t readout with the Lyapunov exponent of about 0.9.
• Turn off Second trajectory to focus on a single path.

1. 1Describe sensitive dependence on initial conditions.
2. 2Explain why a deterministic system can still be unpredictable.
3. 3Observe how parameter changes alter the behavior of an attractor.
4. 4Interpret an exponential growth rate of separation.

Questions teachers ask