LORENZ ATTRACTOR

Explore the famous chaotic system that demonstrates the "butterfly effect." Watch as tiny changes in initial conditions create completely different trajectories.

CONTROL PANEL
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3D CHAOTIC SYSTEM
Real-time 3D chaotic system • Drag to rotate • Scroll to zoom
MATHEMATICAL BACKGROUND

The Lorenz system is defined by three differential equations:

dx/dt = σ(y - x)
dy/dt = x(ρ - z) - y
dz/dt = xy - βz

Where σ, ρ, and β are parameters that control the system's behavior. For certain values, the system exhibits chaotic behavior.

CHAOS THEORY
Butterfly Effect: Small changes lead to vastly different outcomes
Strange Attractor: The system never repeats but stays bounded
Sensitivity: Initial conditions determine long-term behavior
Deterministic: No randomness, yet unpredictable
Applications: Weather prediction, fluid dynamics, economics