Electronic Proceedings of the Ninth Annual International Conference on Technology in Collegiate Mathematics

Reno, Nevada, November 7-10, 1996

Paper C029

Determining an Iterated Function System Interactively

Mark R. Treuden

Department of Mathematics
University of Wisconsin-Stevens Point
Stevens Point, WI 54481-3897
Phone: (715) 346-3734

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Click to access this paper: paper.pdf
Additional file(s) associated with this paper:
  • ICTCM96.IFS IFS codes needed by the program FRACTINT (version 19.5, for DOS)
  • ICTCM96.PAR FRACTINT parameters used to render the images with FRACTINT
  • JUNIPER.DXF vector graphics file


A convincing image of a highly self-similar object can be encoded by using an iterated function system (IFS). Standard examples of this in the literature include ferns, leaves, and trees. The collage theorem gives some indication how such an IFS should be chosen, but to actually find the parameter values for each transformation in the IFS can be a frustrating experience for the student. However, with a vector-based drawing program the student can interactively determine the parameter values of the IFS and easily change them as needed to improve the picture. Examples will be discussed which illustrate how this may be accomplished.

Keyword(s): software, chaos and fractals