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Hi Michael,

The relationship between nature and fractal geometry is a favorite topic of mine.

I am wondering if you could give us a brief preview, overview or synposis of "the latest" developments in this area, so we will have a better feel for the book's coverage of this topic.

Thanks,
Rob

Michael didn't need an introduction, but here is a description of him and his work (from Wikipedia):

Michael Barnsley is a researcher and an entrepreneur who has worked on fractal compression; he holds several patents on the technology. In 1987 he founded Iterated Systems Incorporated, and in 1988 he published a book entitled Fractals Everywhere. He has also published these scientific papers: "Existence and Uniqueness of Orbital Measures", "Theory and Applications of Fractal Tops", "A Fractal Valued Random Iteration Algorithm and Fractal Hierarchy", "V-variable fractals and superfractals", "Fractal Transformations" and "Ergodic Theory, Fractal Tops and Colour Stealing".

Barnsley was one of the founders of a business effort devoted to fractal image compression, 'Iterated Systems'. This company morphed into an 'image archive management' company called 'Media Bin' which appears to have ceased business operations in 2004, after apparently divesting itself of affiliation with Barnsley.

Fractal image compression failed to make an impact on the image data market, principally because its advantages, though real, failed to justify costs of use  as opposed to communal methods invoking jpeg. Faster computer and internet speeds removed most of the objections to use posed by jpeg, thus obviated the need for the far more bandwidth efficient fractal image compression.

Currently (2005) he is on the faculty of the Mathematical Sciences Institute of the Australian National University. Barnsley held a previous faculty position at Georgia Tech.

Actually I think that I have several fractal formulas with the name "Barnsley" in it.   

Are they yours?  The formulas are part of my Ultra Fractal program.