Online Tool Store
Chaos Attractor Visualizer
Interactive 3D canvas visualizer simulating dynamic chaotic systems including the Lorenz butterfly attractor, Rössler attractor, and Aizawa system in real-time.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Dynamic Chaotic Attractor Simulation
Runge-Kutta numerical integration of non-linear differential equations.
Attractor System Type
Lorenz Strange Attractor
dx/dt = σ(y - x)
System Parameters
σ = 10, ρ = 28, β = 8/3
Non-periodic deterministic chaos
Butterfly Effect Context
Sensitive dependence on initial conditions discovered by Edward Lorenz (1963).
How it works
- Select a dynamic chaotic attractor system (Lorenz Butterfly, Rössler, Aizawa Sphere, or Thomas Cyclical).
- The simulator integrates non-linear differential equations at 60 FPS in real-time.
- Watch the rotating 3D phase-space trajectory render glowing gradient paths that never repeat.
- Use the Pause/Resume and Restart buttons to inspect the deterministic evolution from initial seed coordinates.
The formula
Lorenz Equations: dx/dt = σ(y − x), dy/dt = x(ρ − z) − y, dz/dt = xy − βz
Rössler Equations: dx/dt = −y − z, dy/dt = x + ay, dz/dt = b + z(x − c)
FAQ
What is a strange attractor in chaos theory?
A strange attractor is a fractal, non-periodic geometrical structure toward which a chaotic dynamic system evolves over time in phase space. The trajectories never intersect or repeat, yet remain bounded within a defined volume.
What is the Butterfly Effect?
Discovered by meteorologist Edward Lorenz in 1963 while modeling atmospheric convection, the butterfly effect describes how infinitesimal differences in initial conditions yield exponentially divergent long-term trajectories.
How are Lorenz, Rössler, and Aizawa attractors solved numerically?
The continuous non-linear differential equations are integrated over discrete time increments (dt) using numerical approximation techniques (such as Euler or Runge-Kutta integration) on an interactive HTML5 canvas.
What are the classic parameters for the Lorenz butterfly attractor?
The standard parameters that produce the iconic butterfly wings are: Prandtl number σ = 10, Rayleigh number ρ = 28, and geometric factor β = 8/3 (~2.667).
How we compare
| Feature | Online Tool Store | Static textbook images | MATLAB scripts |
|---|---|---|---|
| Real-time 60 FPS rotating 3D canvas | ✓ | ✗ (2D static) | ✓ |
| Multiple chaotic systems (Lorenz, Rössler, Aizawa) | ✓ | Lorenz only | ✓ |
| Zero installation or coding required | ✓ | ✓ | ✗ |