Editing Iterated function system (section)

==The inverse problem==
{{Main|Fractal compression}}

Very fast algorithms exist to generate an image from a set of IFS or PIFS parameters. It is faster and requires much less storage space to store a description of how it was created, transmit that description to a destination device, and regenerate that image anew on the destination device, than to store and transmit the color of each pixel in the image.<ref name="lacroix">Bruno Lacroix. [http://www.collectionscanada.gc.ca/obj/s4/f2/dsk2/ftp01/MQ36939.pdf "Fractal Image Compression"]. 1998.</ref>

The [[inverse problem]] is more difficult: given some original arbitrary digital image such as a digital photograph, try to find a set of IFS parameters which, when evaluated by iteration, produces another image visually similar to the original.
In 1989, Arnaud Jacquin presented a solution to a restricted form of the inverse problem using only PIFS; the general form of the inverse problem remains unsolved.<ref>
Dietmar Saupe, Raouf Hamzaoui.
[https://www.uni-konstanz.de/mmsp/pubsys/publishedFiles/SaHa94.pdf "A Review of the Fractal Image Compression Literature"].
</ref><ref name="kominek">
John Kominek.
[https://web.archive.org/web/20181123231446/https://pdfs.semanticscholar.org/d77b/ffac2560c92771d3756c0e29863a44919d6f.pdf "Algorithm for Fast Fractal Image Compression"].
{{doi|10.1117/12.206368}}.
</ref><ref name="lacroix"/>

As of 1995, all [[fractal compression]] software is based on Jacquin's approach.<ref name="kominek"/>