Most people have heard of fractals. Usually the first thought that comes to their heads when hearing the word, is the sublime and mesmerizing computer generated images accompanied with an array of colours. That’s as much as I knew about them for a number of years.
The few people I know who talk about fractals, usually speak of them in the form of art or make metaphysical speculations on their presence in the very fabric of the universe. Since I knew little about the subject, I usually refrained from making myself heard.
So I finally decided to read up to find out what fractals are and whether they are anything more than pretty pictures. I found and read the following book ‘The Colours of Infinity: The Beauty, The Power and the Sense of Fractals’ which was co-authored surprisingly by Aurther C Clark, The same guy who wrote ‘2001: A Space Odyssey’. I wasn’t a real fan of how they explained some concepts as I found it difficult to follow, so when required I googled the various topics that came up, which I wanted further clarification on.
In the end I am happy to say I have a much better understanding of what fractals are, some of the applications of the them in different fields and even managed to understand some of the maths behind the most beautiful fractal-like sets such as the Mandelbrot and the Julia sets.
First a quick definition:
One notable example in nature is the branches on a tree. A branch has smaller branches coming out of it, those smaller branches have their own smaller ones which can go on for a number of iterations, each being a close remembrance of each other.
A mathematical example would be the Sierpinski triangle . A self-similar set of triangles.
List of Interesting things I learnt about fractals
- The most famous fractal related image is the ‘Mandelbrot set’, it pays tribute to the man who popularized the field. What’s really interesting about the Mandelbrot set is that it uses a single relatively basic formula but generates infinite complexity.
- You can theoretically keep zooming into any part of the Mantelbrot and it will be just as complex with ever smaller and more intricate sub-parts to it. Here’s a zoomed area of the above image or else see the video
- The colors in the above images are arbitrary, and are not really part of the Mantelbrot set. Only the black area is considered part of the set. All the colors basically represent how long it takes for certain values to escape the set.
- Some applications of fractals are very interesting indeed. Here’s a short list of what caught my eyes:
- Allowed better techniques for data compression, especially images.
- Makes estimating the length of coastlines more accurate. The problem was when taking measurements of a coastline, the more detailed the measurement the more zig-zags where measured and the result was vastly different lengths. Fractals came to the rescue.
- Used for special effects in movies to create realistic landscapes on foreign planets. First used in Star Trek II: The Wrath of Khan and Return of the Jedi.
- Fractals exist in nature. I already mentioned the tree structure and coastlines, here’s a few more: