Lorenz attractor simulator
The Lorenz system is a set of three deterministic differential equations. Nearby initial conditions can diverge over time even when the parameters are identical. Its familiar two-lobed trajectory illustrates sensitivity to initial conditions.
A Lorenz trajectory
Two nearby initial states can diverge under the same deterministic equations. This numerical illustration uses RK4; it is not a weather forecast.
ẋ = σ(y−x); ẏ = x(ρ−z)−y; ż = xy−βzσ = 10, ρ = 28, β = 8/3. Blue and orange trajectories use nearby initial states.
Lorenz · Deterministic Nonperiodic Flow, 1963 ↗These are numerical illustrations. Exported values are simulation data, separate from the published human-study data in the research library.
Try this
Change the initial separation between the blue and orange trajectories. Let the simulation run and watch them depart. Resetting the separation restarts both paths from their initial conditions.
What the model leaves out
This is a finite-step RK4 illustration at standard Lorenz parameters. It is not a weather forecast. Numerical rounding and step size also affect computed trajectories.
Where the equation comes from
Two nearby initial states can diverge under the same deterministic equations. This numerical illustration uses RK4; it is not a weather forecast.
Lorenz · Deterministic Nonperiodic Flow, 1963 ↗