Integrate classic ODE and PDE systems in real time — chaos, epidemics, oscillators, ecosystems, and Turing patterns — and see how parameters reshape the dynamics.
Dynamics — Lorenz AttractorLive
RK4 integrator
Controls
A three-variable system of ODEs whose solutions form the iconic butterfly-shaped strange attractor — a textbook example of deterministic chaos.
Data Inspector
Steps8001
IntegratorRK4
final x1.321
final y1.415
final z17.664
Governing equation
x˙=10(y−x),y˙=x(28−z)−y,z˙=xy−2.67z
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
Ordinary differential equations are integrated with a fixed-step fourth-order Runge–Kutta (RK4) scheme; the Gray–Scott reaction–diffusion system uses an explicit finite-difference Laplacian on a periodic grid. Each system exposes its real parameters, so you can drive a pendulum into chaos, tune an epidemic's R₀, or move Gray–Scott between spots, stripes, and mazes.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this dynamical systems simulation tool really free?▾
Yes. Dynamical Systems Simulator runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.