What is the Lorenz Attractor?

The Lorenz Attractor is a set of chaotic solutions to the Lorenz system, discovered by Edward Lorenz in 1963. It exhibits a butterfly-shaped strange attractor where trajectories never repeat but remain bounded in phase space. It's one of the most famous examples of deterministic chaos.

What causes the butterfly effect in the Lorenz system?

Extreme sensitivity to initial conditions causes the butterfly effect. Two trajectories starting infinitesimally close together diverge exponentially, making long-term prediction impossible despite the system being deterministic. This is quantified by a positive Lyapunov exponent.

What are the Lorenz equations?

The Lorenz equations are: dx/dt = σ(y - x), dy/dt = x(ρ - z) - y, dz/dt = xy - βz. The classic parameters are σ=10, ρ=28, β=8/3. These differential equations model simplified atmospheric convection and produce chaotic behavior for certain parameter ranges.

What is a strange attractor?

A strange attractor is a fractal set in phase space toward which trajectories converge but never settle into a periodic orbit. The Lorenz attractor is strange because it has non-integer (fractal) dimension and exhibits sensitive dependence on initial conditions within its basin of attraction.

Home▸Chaos & Dynamics▸Lorenz Attractor Simulator - Chaos Theory, Strange Attractors and Butterfly Effect

🧪 Lorenz Attractor Simulator - Chaos Theory, Strange Attractors and Butterfly Effect

Visualise the Lorenz attractor in real-time 3D. Explore sensitive dependence on initial conditions, the butterfly effect, strange attractor geometry, and deterministic chaos in differential equations.

Chaos & Dynamics2DModerate60 FPS

⚙ Under the hood

This simulation models the Lorenz attractor, a classic example of chaotic behavior in dynamical systems. Users can observe how small changes in initial conditions lead to drastically different trajectories, demonstrating the 'butterfly effect' and illustrating strange attractors.

Lorenz AttractorStrange AttractorsButterfly Effect

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install