Strange Attractors
Integrator: Euler
Lyapunov Map scroll zoom · drag pan · hover λ
λ=
-2.00λ=0+2.00
Cross-Section
X pl.
Y pl.
Z pl.
Traj Color Settings [T] to close
Trajectory Style & Size
Radius / Thickness
Trajectory
drag rotate · scroll zoom
Map Color Settings [C] to close
Offset
Saturation
Linear Scale
Quadratic Scale
Log-mix
α =
Eason Sun, 2026
Settings [Tab]
Integrator
Fast. Use small dt (<0.01) to stay stable.
Theme
UI Scale
Grid Lines
Alpha
Map Resolution
%
Lower = faster render, higher = crisper pixels
Strange Attractor Phase Space Explorer — Eason Sun, 2026
[Tab] to close
Strange Attractor Phase Space Explorer — Controls
Map Navigation
scrollZoom in/out
dragPan
shift+dragStretch axes independently
clickSet initial condition
hoverShow λ value at cursor
Keyboard
EEquation editor
HReset view
SReset stretch
CMap color panel
TTrajectory color panel
TabSettings
XExport map
1This help screen
EscClose any panel
What is the Lyapunov Map?
Each pixel represents an initial condition. Its color shows the Lyapunov exponent λ — a measure of how quickly nearby trajectories diverge.

λ > 0 (orange/warm): chaotic — exponential divergence.
λ < 0 (blue/cool): stable — trajectories converge.

The map axes can be any two system parameters or initial conditions. Choose them in the Axes controls below.
Equation Editor [E]
Enter any 3D autonomous ODE. Use x y z as state variables. Any other letter or Greek symbol becomes a slider parameter automatically.

Choose from built-in attractors: Lorenz, Rössler, Thomas, Halvorsen, Dadras, Aizawa, Chen.
Export [X]
Renders the current map at a custom resolution and copies all parameters in LaTeX or plain text for papers and presentations.
Export Map [X]
Render Resolution
Scale %
Copy Parameters
[X] toggle
System Equations [E]
Presets
Equations — x y z = state  ·  Greek & other letters = params  ·  \pi = constant · \exp(x) for e^x
Parameters — edit initial values
[E] toggle