Collage theorem

In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set. The IFS described is composed of contractions whose images, as a collage or union when mapping the given set, are arbitrarily close to the given set. It is typically used in fractal compression.

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See also

• Michael Barnsley

References

• Barnsley, Michael. (1988). Fractals Everywhere. Academic Press, Inc. ISBN 0-12-079062-9.

External links

• A description of the collage theorem and interactive Java applet at cut-the-knot.
• Notes on designing IFSs to approximate real images.
• Expository Paper on Fractals and Collage theorem