
Product No.
99779 
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Multiple Reduction Copy Machines and Fractals (UMAP)
Frederick Solomon

Mathematics Topic: Linear Algebra, Precalculus 
Application Areas: Mathematics 
Prerequisites: None. 

 ©2000 by COMAP, Inc.  Tools for Teaching 1999  27 pages 

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 Javaenabled browser at http://www.warrenwilson.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 selfsimilarity  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



