Living on Terra-Fractal

Nobody can deny how beautiful nature can be. From massive mountain ranges, raging rivers and diverse forests to something so small as the wings of a butterfly. How can we even begin to understand how nature makes such complex things and builds the world around us? The answer may have been found by perhaps the most unlikely group of people: the mathematicians.

To understand the more complex side to nature, first think of a normal tree. If you follow the trunk upward, you’ll eventually reach several branches. If you follow these branches you’ll reach even more smaller branches. The interesting thing is, if you look at any one branch on the tree, it will look almost exactly as the trunk itself looks, only smaller.

This self replicating sort of pattern is known to mathematicians as a fractal. Look at a lightning bolt. Each branch on the lightning bolt looks just like the original bolt itself. Starting to make the connection to the self replicating branches of a tree? What about a river? Alongside the main river itself, you’ll find smaller rivers branching off which also have small creeks running off them. With all these examples, maybe you’re starting to think that nature’s not so random.

But OK, I can accept a little scepticism. I’ve only explained these tree like shapes so far. What about mountain ranges that don’t look like trees at all? Well actually, fractals explain these as well. If you look at the biggest mountain in a range, it should have a couple of similar, smaller mountains around it. Then you look at the next biggest mountain. Well it too has some similar, smaller mountains around it. There’s only going to be one or two massive mountains (the trunk of the tree) compared to lots of smaller ones (branches). Have a look at this broccoli-like Romanesco. It’s another perfect example of a self similar fractal “mountain range”.

If nature is constructed according to these rules, how can we use this knowledge to our benefit? Well for one, it’s necessary for our phones to have lots of different antennae in them in order to pick up calls,  radio, bluetooth or wireless internet. We don’t really want to be walking around with massive satellite dishes attached to our phones. It was found that if you took an antenna and started folding it up in this    self similar pattern, it works amazingly well even though it’s so small.

It’s also thought that perhaps the universe itself can be described with fractals. Think about distributions of stars in a galaxy. Big ones and small ones, just like the mountain range. Well maybe the galaxies themselves can be distributed like that. The possibilities are endless, all from understanding the world around us and the rules that govern nature.

I could talk on and on about fractals and natural examples. If you’re still interested or just want to see some more pretty pictures, have a look at this website:           http://www.fractalzone.be/gallery.php


3 Responses to “Living on Terra-Fractal”

  1. Scott Lillie says:

    Fractals are pretty mind boggling. We looked at them briefly in Dynamical Systems and Chaos. It’s incredible how so much detail can emerge from such simple mathematical rules. Awesome video on the Star Wars effects!

  2. grills says:

    Hey Nicole,

    Yes it’s definitely true. When they make computer generated images for either video games or animations in films, using fractals makes it that much easier. In the past, it would have been necessary to draw each individual mountain for a certain scene. These days you can generate a whole mountain range with minimal work if you use fractals.

    It doesn’t only have to be applied to scenery either. It took a little while but I finally tracked down this video on youtube.
    https://www.youtube.com/watch?v=1gI6OdnmAGs&feature=player_detailpage#t=714s

    It should already be at almost the 12 minute mark, otherwise just jump to there. Also you might have to load the next video to watch the last part.
    They show how they used fractals in Star Wars episode 3 to make lava. You could think of it as a jet of lava created by the computer is the ‘tree trunk’. Then when fractal techniques are added, the jet of lava is given extra layers of texture and movement which are the little added ‘branches’.

    I won’t go on too much, but I also remember seeing examples of fractals being used for the hair on that big blue monster out of monsters inc. Instead of drawing each hair and discribing it’s movement, fractals can do it all for us.

    If you’ve got any other questions, feel free to ask. I’ll do my best to answer.

    Lloyd

  3. Nicole Darman says:

    Nice post. I heard they use fractals for the mountain ranges when designing and rendering video games because its much cheaper and faster. Do you know if that’s true?