The Collage Theorem
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|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. Also at http://www.cut-the-knot.org/ctk/ifs.html.|
|Levels:||High School (9-12), College|
|Resource Types:||Problems/Puzzles, Articles, Web Interactive/Java|
|Math Topics:||Patterns/Relationships, Fractals, Number Theory|
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