Automatic Generation of Iterated Function Systems
J. C. Sprott
Department of Physics, University
of Wisconsin, Madison, WI 53706, USA
A set of affine mappings with randomly chosen coefficients is
iterated numerically using the random iteration algorithm to produce an
attractor with fractal characteristics. The attractor is tested for
sensitivity to initial conditions, and correlation dimension. In this
a computer can generate a large collection of fractal patterns that are
all different and most of which have considerable aesthetic appeal. A
computer program and examples of its
are provided. Many of the attractors have been systematically evaluated
for visual appeal, and a correlation is found with the Lyapunov
and correlation dimension.
Ref: J. C. Sprott, Comput. & Graphics
18, 417-425 (1994)
The complete paper is available
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Fig. 1. Examples of iterated function systems produced by pairs of
Fig. 2. Results of evaluating 7500 iterated function systems,
that the most visually appealing cases are those with large negative
exponents (L) and with correlation dimensions (F) greater than one.
Fig. 3. Examples of iterated function systems produced by pairs of
affine maps in which the color is determined by one of the variables.
The computer source code ifs.bas
the article is available along with an executable version ifs.exe.