The Exploratorium in San Francisco has a nice little demo of this effect in the form of a "Lorenz Butterfly" that I'm unable to upload here, so I'll give the link:
http://www.exploratorium.edu/complexity/java/lorenz.html
The idea is that two particles can start out in the same spot, but will eventually the difference in their paths becomes greater. This is an example of "sensitive dependence upon initial conditions". It's fun to look at, too.
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Hi, sorry to make the humans do an extra step.