# Automatic Generation of Strange Attractors

J. C. Sprott

*Department of Physics, University
of Wisconsin, Madison, WI 53706*
### ABSTRACT

A pair of coupled quadratic difference equations with randomly chosen
coefficients
is repeatedly iterated by computer to produce a two-dimensional map.
The
map is tested for stability and sensitivity to initial conditions. The
process is repeated until a chaotic solution is found. In this way a
computer
can generate a large collection of strange attractors that are all
different,
and most of which have considerable aesthetic appeal. A simple computer
program and examples of its output are
provided.
Many of the attractors have been systematically evaluated for visual
appeal,
and a correlation is found with the Lyapunov exponent and correlation
dimension.
Ref: J. C. Sprott, Comput. & Graphics
**17**,
325-332 (1993)

The complete paper is available
in PDF format.

Return to Sprott's Books and Publications.

Fig. 1. Examples of strange attractors produced by two-dimensional
iterated
quadratic maps.

Fig. 2. Results of evaluating 7500 strange attractors, showing that
the most visually appealing cases are those with small Lyapunov
exponents
(L) and with correlation dimensions (F) somewhat greater than one.

Fig. 3. Examples of strange attractors produced by three-dimensional
iterated quadratic maps in which the color is determined by one of the
variables.

A variant of the computer source code prog06.bas
from the article is available along with an executable version prog06.exe.
A version of the program is also available as a Java
applet.