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Barnsley's fern

Another very prominent IFS is called Barnsley's fern. The construction is based on the observation that the leafs of a fern themselves look like a small fern. The image is self-explaining:

Please enable Java for an interactive construction (with Cinderella).

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IFS from two similarities $\hookleftarrow$ Contents $\hookrightarrow$ IFS from two Möbius transformations