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.
Statement of the theorem
where is the Hausdorff metric. Then
where A is the attractor of the IFS. Equivalently,
- A description of the collage theorem and interactive Java applet at cut-the-knot.
- Notes on designing IFSs to approximate real images.[dead link]
- Expository Paper on Fractals and Collage theorem
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