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The theoretical foundations of fractal image compression are closely associated with the work of Michael Barnsley, who developed mathematical concepts involving Iterated Function Systems (IFS). Barnsley’s work demonstrated how highly complex shapes could emerge from repeated applications of relatively simple mathematical transformations.

At the same time, public fascination with fractals was growing rapidly because of the work of Benoit Mandelbrot. Mandelbrot showed that many natural structures exhibit self-similarity — meaning that smaller parts resemble larger parts. Coastlines, clouds, mountains, plants, and river systems all contain patterns that repeat across different scales.

Researchers realized that digital images might also contain large amounts of internal redundancy based on self-similarity. This observation led to the development of fractal compression algorithms.

In the late 1980s and early 1990s, Iterated Systems attempted to commercialize the technology and generated considerable excitement in the technology industry. Some enthusiasts even claimed that fractal compression would eventually replace traditional image formats such as JPEG.

However, despite strong theoretical advantages, practical limitations prevented widespread adoption in 20th Century.