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© Copyright 2002, Jim Loy
On the left, we have the famous
Lorenz attractor (drawn using
Fractint and
Paint Shop Pro), discovered by Edward Lorenz.
This is a three dimensional graph (see my rotating animation on the right,
which I created using Animation Shop) of some
fairly simple equations involving x, y, and z:
x'=-sx+sy
y'=Rx-y-xz
z'=-Bz+xy
In these equations, I have used s to stand for sigma. Lorenz set these constants at s=10, B=8/3, and R=28. x, y, and z are plotted on the graph. Then x' becomes the new x, y' becomes the new y, and z' becomes the new z; and it is all replotted. This is done over and over again. Instead of plotting infinitely many points, the program draws a line between successive points of the graph, approximating the curve. The graph never intersects with itself.
While the Lorenz attractor is interesting (and surprisingly complicated) in itself, it originally came from a model for convection currents in the air. And it may give clues to why the weather is so unpredictable.