Applications of Fractals
In December 1992, Microsoft released a compact disk entitled the Encarta Encyclopedia. It contains thousands of articles, 7000 photographs, 100 animations, and 800 color maps. All of this is in less than 600 megabytes of data. How was it possible? The answer lies in the mathematics of fractal data compression.
Consider the Mandelbrot Set. A color full-screen GIF image of it occupies about 35 kilobytes. However, all you need to store it is the formula z = z^2 + c, which takes no more than 7 bytes. That’s a 99.98% compression – talk about efficiency! Well, maybe if it works for the Mandelbrot Set... it could work for a flower diagram, a map of Africa, or a photo of Kennedy as well! The goal is too find functions, each of which produces some part of the image. For a complex image that is not a fractal, you might need hundreds of such functions. Yet, it would still take up less space than hundreds of thousands of colored pixels. IFS are the functions usually used for compressing data. The mathematical foundation of the image compression was established by Michael Barnsley, who is the founder of IFS fractals as well.
|Fractal Image Compression
A reference on image compression using fractals