The Mathematics of Beauty > Timeline > 1987 - Michael Barnsley - Fractal Compression

Michael Barnsley led development of Fractal Compression in 1987, and was granted several patents on the technology. The most widely known practical Fractal Compression algorithm was invented by Barnsley and Alan Sloan. Barnsley's graduate student Arnaud Jacquin implemented the first automatic algorithm in software in 1992. All methods are based on the fractal transform using iterated function systems. Michael Barnsley and Alan Sloan formed Iterated Systems Inc. in 1987 which was granted over 20 additional patents related to fractal compression.

A major breakthrough for Iterated Systems Inc. was the automatic fractal transform process which eliminated the need for human intervention during compression as was the case in early experimentation with fractal compression technology. In 1992 Iterated Systems Inc. received a $2.1 million government grant to develop a prototype digital image storage and decompression chip using fractal transform image compression technology.

The Barnsley Fern is a fractal named after the British mathematician Michael Barnsley who first described it in his book Fractals Everywhere. He made it to resemble the Black Spleenwort, Asplenium adiantum-nigrum.

The fern is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Like the Sierpinski triangle, the Barnsley Fern shows how graphically beautiful structures can be built from repetitive uses of mathematical formulas with computers. Barnsley's book about fractals is based on the course which he taught for undergraduate and graduate students in the School of Mathematics, Georgia Institute of Technology, called Fractal Geometry. After publishing the book, a second course was developed, called Fractal Measure Theory. Barnsley's work has been a source of inspiration to graphic artists attempting to imitate nature with mathematical models.

The fern code developed by Barnsley is an example of an iterated function system (IFS) to create a fractal. He has used fractals to model a diverse range of phenomena in science and technology, but most specifically plant structures.

"IFSs provide models for certain plants, leaves, and ferns, by virtue of the self-similarity which often occurs in branching structures in nature. But nature also exhibits randomness and variation from one level to the next; no two ferns are exactly alike, and the branching fronds become leaves at a smaller scale. V-variable fractals allow for such randomness and variability across scales, while at the same time admitting a continuous dependence on parameters which facilitates geometrical modelling. These factors allow us to make the hybrid biological models... ...we speculate that when a V -variable geometrical fractal model is found that has a good match to the geometry of a given plant, then there is a specific relationship between these code trees and the information stored in the genes of the plant."     - Michael Barnsley

- Wikipedia

Return to Timeline