Lorenz Attractor Simulation
The butterfly-shaped strange attractor
The Lorenz Attractor — a "butterfly" shaped trajectory that never repeats. σ=10, ρ=28, β=2.67. The foundation of chaos theory.
What Is Lorenz Attractor?
The Lorenz system is a deterministic nonlinear dynamical system that produces a strange attractor. The trajectory never exactly repeats, but remains confined to a characteristic butterfly-shaped region.
What To Observe
- The path loops around one lobe, then switches unpredictably to the other.
- Even with fixed parameters, long-term behavior remains sensitive to initial conditions.
- The drawing accumulates structure while never settling into a simple periodic orbit.
Related Simulations
Mandelbrot / Fractal Explorer Interactive Mandelbrot set rendering Cellular Automata Conway's Game of Life and emergent patterns Logistic Map / Bifurcation Diagram Period-doubling route to chaos in a nonlinear map Percolation Simulation Spanning clusters and threshold behavior Flocking / Boids Algorithm Emergent flocking from local motion rules Reaction-Diffusion Patterns Pattern formation from reaction and diffusion Lissajous Figures Parametric curves from orthogonal oscillations Moiré Patterns Large fringes from overlapping line grids
Try These Experiments
- Reload the page and compare how small initialization changes alter the trajectory.
- Discuss the difference between deterministic equations and predictability.
- Pair this with the double pendulum simulation for a chaos unit.
Real-World Applications
- Chaos theory education
- Weather-system intuition
- Nonlinear dynamics coursework