3D visualization of ODE systems and strange attractors
LMB — rotate camera. Wheel — zoom. RMB — pan. Brush — click the scene to add a trajectory.
Presets (examples with parameters)
Axes x, y, z are phase. LMB rotates, wheel zooms, RMB pans.
System
Quick reference
An autonomous system in \(\mathbb{R}^3\) can be chaotic. The Lorenz attractor at the classic parameters:
\[ \begin{cases} \dot{x} = \sigma(y-x) \\ \dot{y} = x(\rho-z)-y \\ \dot{z} = xy-\beta z \end{cases} \]A strange attractor is a bounded attracting set with fractal structure and sensitive dependence on initial data.
Plot the Lorenz attractor in a 3D calculator
ODEPLOT integrates \(\dot x,\dot y,\dot z\) and shows spatial trajectories you can rotate and zoom.
Presets: Lorenz, Rössler, Chen. Change coefficients and the starting point; save the scene as PNG.
What you can do on this page
On this page you can open the scene full screen, rotate and zoom phase space, animate system parameters and a stream of points, and save the scene as PNG.