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Reference.org
Collage theorem
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the collage theorem characterises an <a href="/facts/Iterated_function_system/j56g6yEM">iterated function system</a> whose <a href="/facts/Attractor/FAx5Db4w">attractor</a> is close, relative to the <a href="/facts/Hausdorff_metric/3tKbFmKu">Hausdorff metric</a>, to a given set. The IFS described is composed of <a href="/facts/Contraction_mapping/VSu4qNqa">contractions</a> whose images, as a collage or <a href="/facts/Union_(set_theory)/KVVXKfWl">union</a> when mapping the given set, are arbitrarily close to the given set. It is typically used in <a href="/facts/Fractal_compression/d2qUg7sc">fractal compression</a>. </p>