7.1 Reconstruct the Lorenz attractor

  • Package fractal includes the 3 dimensions of the Lorenz system in the chaotic regime.
    • Run this code rgl::plot3d(lorenz) with both packages loaded to get an interactive 3D plot4 of this strange attractor.

We’ll reconstruct the attractor based on just dimension X of the system using functions from package fractal, be sure to look at the manual pages of these functions.

Package fractal and package nonlinearTseries use functions with similar names, do not load them together.

  • Use lx <- lorenz[1:2048,1] to reconstruct the phase space based on lx.
    • Find an optimal embedding lag using timeLag(), use method = "mutual".
    • Find the embedding dimension, using FNN()
    • Embed the timeseries using embedSeries().
    • Plot the reconstructed phase space. (You’ll need to use as.matrix() on the object created by embedSeries())
      • Use rgl::plot3d() to plot the reconstructed space.

  1. You’ll need the X Window System for interactive 3D plotting. This Linux desktop system comes installed in some way or form on most Mac and Windows systems.You can test if it is present by running rgl::open3d(), which will try to open an interactive plotting device