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.