#### The Lorenz Attractor

Here's a plot produced by our *lorenz*
program, with the viewing angle
β = 0 and the Rayleigh parameter
*r* = 25. The *x*-axis is
horizontal; the *z*-axis is vertical. For this plot,
*y* = 0.

Note that this plot is initiated near
*x* = 2.5,
*y* = 0,
*z* = 0.5; the subsequent
trajectory of the plot is very sensitive to this
initial position. For example, the sign of
*x* reverses at unpredictable times.

The first three equations in the white panel are those displayed by Lorenz in his famous paper. See Eqs. 25-27 on this paper's sixth page.

The lower three equations, which are those used in
our program, are equivalent to Lorenz's original
equations, but with the variables *x*,
*y* and *z* simply scaled to ensure
that the size of the plot does not grow or shrink
when the Rayleigh parameter *r* is
increased or decreased.

A tar file containing the source code for the
*lorenz* program is available here. It is designed to be
compiled and run primarily on Linux machines, for
which the *xterm* terminal is available.
(The *lorenz* program must be run from an
*xterm*.) It may also be compiled and run
on Windows machines, where it requires the
installation of three *Cygwin*
packages—not difficult. Detailed
instructions are included with the source code.

The program, which I first wrote many years ago as an exercise, is designed to be educational in that it allows for considerable user interaction. One may increase or decrease the Rayleigh Number, or change the viewing angle of the three-dimensional attractor, or select an initial point for the plotting of the attractor, all while the plotting is taking place. It's not a large program, and easy to compile and run.