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.
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.
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
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:
<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>