Some methods for the Lorenz 63 system in Octave/Matlab
lorenz63ensemble-movie.m - Generates sequence of frames of an ensemble of points in 3-space evolving under the dynamics of the Lorenz 63 system. After the script is run, the images can be converted to a movie using, for example, ffmpeg: ffmpeg -r 20 -i pix/lorenz%04d.png -vcodec ffv1 -sameq pix/lorenz_ensemble.avi
The above script was used to generate this Youtube video.
spaghetti-plot.m - Generates a spaghetti plot showcasing the chaotic nature of the Lorenz 63 system. Several solutions are plotted in time starting from nearly identical initial conditions; the trajectories slowly diverge and eventually hit a sudden rapid divergence.