Fractal compression is a lossy compression method used to compress images using fractals. The method is best suited for photographs of natural scenes (trees, mountains, ferns, clouds). The fractal compression technique relies on the fact that in certain images, parts of the image resemble other parts of the same image. A lossy data compression method is one where compressing data and then decompressing it retrieves data that may well be different from the original, but is close enough to be useful in some way. ... Image compression is the application of data compression on digital images. ... The boundary of the Mandelbrot set is a famous example of a fractal. ... The coniferous Coast Redwood, the tallest tree species on earth. ... Mount McKinley (Denali) in Alaska (USA) has the largest visible base-to-summit elevation difference on Earth. ... Classes Marattiopsida Osmundopsida Gleicheniopsida Pteridopsida A fern, or pteridophyte, is any one of a group of about 20,000 species of plants classified in the Division Pteridophyta, formerly known as Filicophyta. ... Cumulus of fair weather Different cloud types A cloud is a visible mass of condensed droplets or ice crystals suspended in the atmosphere above the surface of the Earth or another planetary body. ...

Michael Barnsley is the principal researcher who has worked on fractal compression (1988), and he holds several patents on the technology. The most widely known practical fractal compression algorithm was invented by Arnaud Jacquin in 1991, although Barnsley and Alan Sloan took out the patent (US. 5,065,447) on this method also. All methods are based on the fractal transform using iterated function systems. Michael Barnsley is the researcher and entrepreneur who has worked on fractal compression; he holds several patents on the technology. ... 1988 (MCMLXXXVIII) was a leap year starting on Friday of the Gregorian calendar. ... A patent is a set of exclusive rights granted by a state to a person for a fixed period of time in exchange for the regulated, public disclosure of certain details of a device, method, process or composition of matter (substance) (known as an invention) which is new, inventive, and... The fractal transform is a technique invented by Michael Barnsley to perform lossy image compression. ... Menger sponge, created by using IFS. Iterated function systems or IFSs, are a kind of fractal which were conceived in their present form by John Hutchinson in 1981 and popularized by Michael Barnsleys book Fractals Everywhere. ...

Fractal compression appeared to be a promising technology in the late 1980s, when in some circumstances it appeared to compress much better than JPEG, its main competitor at that time. However, fractal compression never achieved widespread use. The patent issue may have been a problem (JPEG can be used without any patent royalties), and fractal compression is much slower to compress than JPEG. (JPEG decompression seems to take about the same time as fractal decompression). Also, the improved compression ratio may have been an illusion. Fractal compression only has a large advantage over JPEG at low image quality levels, which is usually undesirable. The claim that fractal compressed images, when enlarged beyond their original size, looked better than similarly enlarged JPEG images seems also to have been an irrelevant distinction. In computing, JPEG (pronounced jay-peg) is a commonly used standard method of lossy compression for photographic images. ...

It also has turned out that the most impressive examples of fractal compression require considerable human intervention: the process of generating an image from its fractal representation is easy to automate, but reversing the procedure to generate an optimal fractal representation of an image is highly non-trivial. Most real-world images have heterogenous mathematical properties; for instance a photograph in which mountains and clouds and trees might be represented by several classes of fractal representation. Barnsley's collage theorem proves that for a large class of real-world images, compact fractal representations must exist; it does not provide a general-purpose algorithm for the construction of such representations. In practice, to achieve high image quality with compression ratios that significantly exceed those of JPEG requires significant amounts of human effort.

Today fractal compression seems to be even less relevant, with wavelet compression outperforming it in most applications for those willing to accept the patent situation. JPEG is still widely used. Wavelet compression is a form of data compression well suited for image compression (sometimes also video compression and audio compression). ... In computing, JPEG (pronounced jay-peg) is a commonly used standard method of lossy compression for photographic images. ...

See also

• Fractal
• JPEG 2000 - Modern image compression method

The boundary of the Mandelbrot set is a famous example of a fractal. ... JPEG 2000 is a wavelet-based image compression standard. ...

See also

• Resources on fractal compression
• Fractal Papers Leipzig Collection
• Fractal Image Compression for Spaceborne Transputers