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Fractal Power

October 11, 2011

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:

A complex geometric pattern exhibiting self-similarity  in that small details of its structure viewed at any scale repeat elements of the overall pattern.

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

  1. 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.
  2. 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
  3. 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.
  4. 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.
  1. Fractals exist in nature. I already mentioned the tree structure and coastlines, here’s a few more:
  • Romanesco broccoli

    romanesco broccoli

  • Ferns [see also Barnsley Fern]

    Natural fern fractal

  • Snowflakes [See also Koch snowflake]

    Snowflake fractal

  • Mountains from above

    Fractal mountains Tibet

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5 Comments leave one →
  1. October 18, 2011 6:31 pm

    Yes! Win.
    😀
    I personally find some of fractals’ most fascinating practical (and personal favourite) applications include:
    – Aesthetic pleasure through visual art
    – Generation and fundamentals of music
    – Basic understanding of how fractal patterns occur within day to day life in the sense of cause & effect, time, nature, and behaviour

  2. October 18, 2011 10:32 pm

    Medical applications of fractals in microsurgery are another really fascinating observation!
    I highly recommend you watch Season 6 of Futurama. I’ve been pleasantly surprised by its new concepts! Ever since that killer bees episode, the writers have taken a more existentially psychotropic perspective of the future it seems.

    • October 19, 2011 8:51 am

      I really need to get into futurama again, i don’t even know when I stopped watching the show.
      I haven’t heard of microsurvery applications. care to expand?

  3. December 16, 2011 9:57 am

    Basically, fractal-based mathematics is used to determine such things as resolution, zoom required for a particular area, and following patterns (we are essentially fractal-based life forms) whilst predicting growth and death, movement, etc. of cells and such based on these fractal-based calculations.

    • jaado permalink
      April 27, 2012 12:32 am

      this conversation ended far too quickly …..it needed some fractal branches

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