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.
![[Figure 1]](203fig1.gif)
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.
![[Figure 2]](203fig2.gif)
Fig. 3. Examples of strange attractors produced by three-dimensional
iterated quadratic maps in which the color is determined by one of the
variables.
![[Figure 3a]](203fig3a.gif)
![[Figure 3b]](203fig3b.gif)
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.