What the Hell are Fractals?
Fractal posters are the only thing of beauty in many a student household, providing visual respite amongst the festering bowls and rotten sofas. But what exactly are fractals? Josh Davies finds out why they're so pleasing.
It’s almost like mathematicians don’t want us to understand them, what with their funny little symbols and imaginary numbers. It’s as if they just don’t want us to be part of their crew. But we're here to crack fractals.
Okay, let’s start with the basics: what the hell are fractals?
Hold your breath for a moment. They’re basically graphs which, however much you zoom in, will always have a complex pattern. A curve for example will turn into a straight line if you zoom in enough but these things will stay curvy. You can also divide a fractal into lots of parts and each of these will look roughly like the whole thing.
Don’t worry if you’re lost already – I asked a physics PhD student to explain these things to me and when I left him I had to spend a week eating ice cream and watching cartoons before my brain recovered (or was that just because I am a lazy student?).Perhaps the most important thing about fractals is that if you type “fractals” into the image search engine in Google you get lots of pretty pictures. The fact that we find these pictures pretty has been studied by scientists, who say that our brains find the symmetry of them pleasing. In my opinion it’s just an excuse for the scientists to spend all day staring at them.
Where did fractals come from?
The word ‘fractal’ came into common usage in 1975 thanks to a guy called Benoît Mandelbrot, although the idea had been kicking around since the 17th century. Sadly, computing power in the 1600s just wasn’t up to scratch so the scientists of the day couldn’t really create them. But since modern day mathematics has got stuck into them, people have been finding fractals all over the place. Even broccoli isn’t safe, nor in fact, is the coastline of the UK.
It works something like this: imagine looking at the UK coast line from space, then imagine looking at it from up at 30,000ft in a plane; its still the same coast line but you can see loads more detail. Then imagine looking at it from a sunny (probably more likely rainy) beach. You can see even more detail from this level. This makes it a fractal.
|
An interesting property of some fractal patterns is that their circumference is infinite but they define a finite area - check out Koch's snowflake to see how.
Hang on, there’s more
Did somebody say fractals had got to something do with pi? Yes, I did in fact. Just then.
Fractals can be used for all sorts of cool things (obviously depending on your definition of cool). One of these is assessing the randomness of something. I know, “randomness of something” sounds completely made up, but bear with me.
For example, the numbers of pi are thought to be random (or more correctly, don’t follow a pattern). A fractal can actually be used to measure this. The maths behind it is quite complicated; very complicated in fact. But using fractals, mathematicians have proved that the numbers of pi are actually more random than numbers produced by a computer random number generator. Random hey?
So are fractals actually useful?
Once scientists found out you could use fractals to measure how random things are, they went a bit crazy – I mean really crazy. They started measuring how random lots of things are.
One study looked at the movement of the ball during a football computer game. I really hope someone didn’t get paid for this research. It can’t be just me who finds this about as useful as a glaciologist in 200 years time.
Even weirder, a group from Spain discovered you could find fractals in pepper plants. They stressed out the pepper plants (by making them watch non-stop episodes of Pop Idol, no doubt) and then measured the veins on the surface of the pepper. They found that the veins on the stressed peppers didn’t grow as randomly as normal peppers. Once again, essential knowledge for everyday life.Finally, the same Spaniards, after getting bored with peppers thought that they would look at fractal behaviour in mountain goats - a progression any normal person would make. They found that stressed (by stressed they mean infected with parasites or pregnant – some people might argue these are one and the same) goats act less randomly than non-stressed goats.
So are fractals useful? Tentatively, I’d go for ‘no’.
Other things that have recently been studied using fractal analysis:
- The shape and texture of women’s breasts (Nguyen & Rangayyan 2005)
- The microfiltration of activated sludge (Meng et al. 2005)
- People’s self esteem (Delignières 2004)
- Drainage networks on Mars (Stepinski et al. 2004)
- The permeability of soil (Yu & Liu 2004)
- Women’s contractions during labour (Oczeretko et al. 2004)
- The movement of narwhals (Laidre et al. 2004)
- The roughness of steel (Kang et al. 2004)
- Changes in people’s breathing rates (Fadel et al. 2004)
More articles from Josh:
- Day in the Life - Living as Labradorite
- On your bike - Destination Comet
More articles to expand your brain:
- Get to know - Genetic modification
- Get to grips - Didgeridoos
- Get to work - Nuclear fusion
Randomness at our Facebook group.
Share this
