The Fractal Factor

They’re in the sky, on the ground, in nature, clothing, special effects and even your cell phone. They’re incredibly simple yet extraordinarily complex. The closer you get to some of them, the further away they seem. They are fractals and they’re everywhere.

Fractals are complex, irregular, endlessly repeating geometric shapes. They can be easily created on a computer but also occur naturally. The classic example is a tree.

It’s Only Natural to Love Fractals

When you look closely at a tree, you’ll see a main section, with branches protruding outwardly from it. Each branch, in turn, is like a mini-tree, with sub-branches sprouting off the main branch. Each sub-branch may also contain a sub-branch. In other words, the tree shape repeats throughout the tree.

Another example is a coastline, which has a certain irregularity or “crinkliness” to its shape. You’ll see the same degree of crinkliness when viewing the coastline from 1 metre, 100 metres, a kilometre or even 10 kilometres – the overall pattern remains the same.

Mountains, flowers, clouds, plants and snowflakes – all of these naturally occurring things are fractals. However, it’s only recently that fractals have been recognized as much more than just pretty patterns. They have real, practical applications in both science and mathematics.

Fractal-shaped antennas are used in mobile devices such as cell phones. It’s been scientifically proven that this type of antenna shape is the most efficient at receiving the widest variety of signals. Without it, your cell phone would resemble a porcupine because it would require so many different antennas.

Many cinematic special effects use fractals. The spectacular lava effects in the finale of the last Star Wars film, Revenge of the Sith, were generated using fractals. Fractals are also used in design, engineering and medicine.

Computer-generated fractals have a particularly unusual property: no matter how much you magnify them, the level of detail does not change. You can see an animated example here.

Info-Fractals

New technology has unknowingly fractalized information. The best example of this is Wikipedia. Open any major topic and you’ll see it’s very detailed and contains dozens, if not hundreds, of hyperlinks. Click the hyperlink within this topic, and it takes you to another detailed topic, again with its own set of hyperlinks. As with fractals, the level of detail remains about the same no matter how much you “zoom in”. This fractalization does not just exist with websites. A complex online help system also allows you to move from one topic to another, with little or no diminishment of detail.

Just as fractals have no real start or end, neither do modern information structures. Although technically both Wikipedia and an online help system have a first and last topic, from the user’s perspective, they do not. Users rarely read documentation linearly – they go directly to the topic they need, perhaps follow some links to get additional information and then they leave. Documentation is not a novel.

Modern documentation, therefore, clearly resembles fractals. However, there is another more important similarity, and to understand it, you need to look at the history of fractals.

Math Wars

Benoît Mandelbrot (1924-), is considered the father of fractals. When he first presented his theories, the mathematical community did not take him seriously. They thought the shapes he created were “pretty” but had no practical applications and therefore did not represent genuine mathematics.

These mathematicians were trapped in their traditional, Euclidean view of mathematics: straight lines, simple curves and basic shapes. They simply could not fathom a math that was so irregular. Many years would pass before other mathematicians finally recognized Mandelbrot’s work as genuine mathematics.

Believe It or Not


Our profession suffers from similar disbelief. It’s held by writers who are unable to accept the new way of creating information, specifically XML, where all information is classified by tags and which separates the form from the content.

XML is as different from traditional documentation as fractals are from traditional mathematics. As an example, you may be used to this way of writing:

Printing a Page (Heading 3 paragraph style)

1. From the File menu, select Print. (Numbered paragraph style)
2. Select your print options. (Numbered paragraph style)
3. Click Print. (Numbered paragraph style)
The document prints. (Body paragraph style)

Now try this way of writing:

<procedure title>Printing a Page</procedure title>
<step>From the <UI element>File</UI element> menu, select <UI element>Print</UI element>.</step>
<step>Select your print options.</step>
<step>Click <UI element>Print</UI element>.</step>
<result>The document prints.<result>
Ugly, isn’t it? There’s no formatting or paragraph styles, just tags. Note that this is an extremely simple example. Still, many writers will balk at this and say it’s not really technical writing but “programming” or “coding”.
An Inconvenient Truth
Just as traditional mathematicians initially refused to accept fractals as actual mathematics, many writers are unable to accept XML as actual information development. However, XML is, in fact, information development in its purest form, because it separates the form of the information (the fonts, point sizes, formatting and layout) from the actual content. In addition, XML allows you to modify, manipulate and manage information in ways that are simply impossible using traditional documentation methods.
The choice is ours: we can continue our old ways, or we can change. If you’re struggling with the new ways, then remember the lowly fractal the next time your cell phone rings.
If it weren’t for one person challenging the system, you’d never be able to get that all-important call.
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One thought on “The Fractal Factor

  1. Paulm

    I enjoyed this article…maybe it is my mathematics background. I agree that XML is just another way of encoding content. We have used many methods over the years, but standards, such as XML, can open many other options to us. For example, we could consider beuilding on content created by others so we expand our knowledge and avoid duplicating efforts of others.

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