Lorenz Strange Attractor

Interactive study of Edward Lorenz's foundational non-linear ordinary differential equations. Demonstrates the butterfly effect, dual orbital manifolds, Runge-Kutta numerical integration, and real-time Lyapunov divergence of two starting trajectories perturbed by Δx₀ = 10⁻⁵.

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60 FPS • Canvas 2D

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Live Parameters

Prandtl (σ) 10

Prandtl number representing fluid viscosity

Rayleigh (ρ) 28

Rayleigh number representing convective driving force

Mathematical Formulation

50 chars high

Analytical Equation

\frac{dx}{dt} = \sigma(y - x), \quad \frac{dy}{dt} = x(\rho - z) - y, \quad \frac{dz}{dt} = xy - \beta z

Compact Formula

dx=s*(y-x)*dt; dy=(x*(r-z)-y)*dt; dz=(x*y-b*z)*dt;

Renderer Logic

// Lorenz Attractor RK4 Integration
const dx = sigma * (y - x);
const dy = x * (rho - z) - y;
const dz = x * y - beta * z;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#chaos-theory #dynamical-systems #lorenz-attractor #butterfly-effect #differential-equations #math-study

Author: Chaos Dynamics Core Target: 60 FPS

Lorenz Strange Attractor

Live Parameters

Mathematical Formulation

Mathematical Tags

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