Multiple Reduction Copy Machines and Fractals (UMAP)

This module uses the idea of the Multiple Redcution Copy Machine (MRCM) to explain iterated function systems and fractals. The purpose is not to develop the theory completely but to explain enough in order to create fractals on the computer. The module describes computer animation that is easy to use but requires some basic understanding of underlying theory. The computer animation is a Java applet that can be accessed on the Internet with a Java-enabled browser at http://www.warren-wilson.edu/~fsolomon/ZZFract.html. The animation allows graphical input of the transformations defining the fractal - the lenses, as they are called in the terminology of the Multiple Reduction Copy Machine. Using the animation while reading this module will provide much insight into the nature of self-similarity - a central defining characterization of fractals.

Table of Contents:

INTRODUCTION

DEFINITIONS OF TERMS AND SOME EXAMPLES

SPECIFYING THE LENSES

EXAMPLES

CREATING FRACTALS

USING THE PROGRAM

EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR