Attractor Reconstruction

The Setting:
The equations are solved, the attractor created.
X, Y, and Z are all quite elated.
But during the night, devious crooks steal the show.
taking Z and X, leaving Y crying "Noooo!"
But you arrive on the scene donning Sherlock Holmes' cap,
claiming you can recover Z and X in a snap.
All you must do is find τ (the Y-lag)
to bring X and Z slowly out of the bag.
For they are attracted to Y don't you know.
The picture appears coming out of the snow.

Your mission:

Choose a system (Lorenz or Rossler) and a time lag for Y.
Try to recreate the 3-D Chaotic attractor from only one variable.


Time Gap:
τ =


High resolution
Long time


To create these datasets, the system was simulated until t=5 to remove transient effects and then to time t at a fine resolution with y-values stored at dt time intervals. For the high resolution dataset, t=100 and dt=0.001. For the long time dataset, t=10000 and dt=0.1.

Note: You will only be able to see a 2-D projection of the attractor. One could create a 3-D version of this lag process plotting y(t), y(t+τ) and y(t+2τ).