Here is a sequence of 14 views of the Lorenz attractor;
you'll need 3D glasses as described previously.
From frame F-8, you can easily see a "tail" sticking out
from the attractor towards the right; this is actually the begining of the particle's path. The particle is rapidly pulled into the near group of spirals, then goes up over the top once before twisting over to the far group.
You can see the "twist over" in the first few frames: watch the top of the near spiral as it falls down to the left, then swoops in close to
the middle of the second batch of spirals. There appear to be about five such cross-overs, before the particle's trajectory was halted.
It is easy to see the point at which the trajectory was halted
in frames 4 and 5, in the "open area" in the middle of the righthand spiral.
Try moving the cursor around the image, to see if it appears to be
behind some parts of it and in front of others.
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© 2001 by Chip Ross Associate Professor of Mathematics Bates College Lewiston, ME 04240 |