Dstool supports the convenient display of the evolution of isoriented (edges parallel to coordinate axes) n-cubes or their boundaries under the flow of a dynamical system.
To see this feature, first reload the Lorenz system defaults
using the procedure described in Section 1.2.12.
Now open up the Multiple Orbits window by selecting (with )
the Multiple... menu entry under the
panels menu button of the command window. The lengths of the
sides of the cube may be edited in the Size column at the bottom of
the panel, and the number of division points along each edge in the
Number column. In the Size column, change the x and y
entries to 5. In the Number of Points column, change these two
(x and y) entries to 20. By default, the Load: choice box
should be set to Rectangle indicating that only the boundary of the
specified n-cube will be evolved; selecting Region here would also
include a mesh of interior points of the specified n-cube. Click
on the Load Points button near the top of the Multiple
Orbits panel. The message 76 initial points loaded will appear.
(See figure
.)
Before actually evolving the rectangle, make sure you have the Orbits panel and a 2-D Image window open (with x and y as coordinates displayed.) Recall these are summoned by menu entries of the Panels and View menu buttons respectively on the main Command window. On the Orbits panel, edit the Stop text field (to the right on the third line) to 1 instead of the default 5000.
Now back on the Multiple Orbits panel, click
on
Forwards. In the view window, you will see the original rectangle
and its evolution one time step later. Click on Continue several times
and you will see the rectangle evolve towards the line x=y.
(Figure
)