The Collage Theorem
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http://www.cuttheknot.org/ctk/ifs.shtml  


Cut the Knot!, Alexander Bogomolny  
To find an IFS whose attractor is "close to" or "looks like" a given set, one must endeavor to find a set of transformations  contraction mappings on a suitable set within which the given set lies  such that the union, or collage, of the images of the given set under transformations is near to the given set. The applet supplied for this exploration was inspired by Barnsley's celebrated depiction of the Black Spleenwort fern... An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem, one not stated directly since the applet is intended to be such that the right answer to an as yet unstated problem should be easy to surmise.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles, Web Interactive/Java 
Math Topics:  Patterns/Relationships, Fractals, Number Theory 
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