Was promoted in the early 1990's as the future of
digital image compression. The basic idea was, given an
image, to find the particular
fractal or combination of fractals that would generate the image after a few
iterations of the
fractal. The way to do this is to find bits of the
image that were
self-similar, but at different scales. For example, if you had a picture of
clouds, then the edge of the cloud looks much the same if you look at the cloud or if you look at a tiny piece of it. So you say something like "this little bit of cloud has the same shape as the big one, only smaller", and you only have to store a few little pieces of information about how to generate the big cloud and that was it. This would give a huge
compression ratio, since you wouldn't have to store millions of
pixel values, rather just a few equations, which, when run
iteratively on itself a few thousand times, would generate the original image. If you wanted a rough image, you would only
iterate a few times.
The other purported advantage was that you could decompress the image at a higher resolution than you compressed the image at, the "fractal nature" of the encoding would interpolate in a more natural manner than simply enlarging the image.
The problem is that it hasn't come to fruition. The main problems were that:
- There is no good algorithm for working out the fractal for an image. In fact, the best algorithm so far developed is the graduate student algorithm (this is serious, that's what the algorithm is called). It was developed by Michael Barnsley. It works like this.
- Get the image you want to compress.
- Put a graduate student in fractal mathematics with a computer and said image in a room.
- Provide lots of pizza and beverages.
- Lock door.
- Do not let graduate student out until he comes up with a good fractal for the image.
Functional, but, unfortunately, not very cost-effective.
Michael Barnsley, his company Iterated Function systems Inc, his students and staff have patents on anything that's even remotely useful in the area. To be really successful as a graphics format, you usually have to be open.
Other compression technologies, in particular wavelet compression, have surpassed it in the mean time, overcoming the problem with Fourier transform-based methods, like JPEG, while at the same time improving the compression ratio. Current state of the art fractal techniques and usable wavelet techniques are pretty much on par in terms of compression ratio and image quality. In fact, the latest version of JPEG, JPEG2000 uses wavelets.
Don't count it out yet, but it doesn't look like fractal image compression will be widely available for some time.