Fractals and Image File Formats

While sick in bed yesterday, I watched part of a very interesting program called “Colors of Infinity” The host was Sir Authur C. Clarke. Yes that Authur, whom anyone growing up in Kenya in the early 80s will remember as the host of the very popular series Arthur C. Clarke’s Mysterious World.

The show, “Colors of Infinity” was about fractals and the mathematics behind fractal geometry. At first I was kind of watching with half interest, till they started talking about the most famous of the fractals sets called the Mandelbrot set. This was the most fascinating part of the whole show.

The show explored the mathematical formula behind the Mandelbrot set and how it’s being used for data compression. As an example, Sir Authur mentioned the spy satellites up higher in the stratosphere than even the weather satellites, and transmitting images and data that are way more detailed than the weather data. Then using two images as examples, he showed the difference between an ordinary GIF type image and one that had been created using fractal compression. The difference was pretty astounding. As he zoomed into the GIF image, the pixilation showed up immediately. However, with the second image, he zoomed into the picture again and again and the image was still very clear.

This is really amazing when you think about it because this means you can potentially create “infinite” resolution images that are really relatively decent sized. This I think is what Authur was talking about with the spy satellites. These satellites send back really, really high resolution images that very detailed, and so the compression requirements and the bandwidth requirements can be a major constraint on the delivery channel.

There are a large number of applications for fractal geometry, and image/data compression is just one of them. I will write again on this topic later after I have researched a little more. sometime during the Christmas break.

Want to learn more? Checkout this resource on image file formats. Also, here is more info on the Mandelbrot set.