Recommended Reading
You may have heard at some time or another phrases like ‘The Butterfly Effect’ or ‘Chaos Theory’.
What do they mean exactly and are they a serious aspect of everyday life?
Nature behaves in many ways we can describe mathematically. Once we can do this, in theory we should be able to forecast what it will do next. For example, predicting the weather, major economical events or earthquakes etc.
A branch of mathematics which is relatively new (i.e. only a few hundred years) attempts to do just this. It’s called Chaos Theory – and it’s basically the study of a certain family of equations which are very easy to define but which create very complex patterns (called fractals) when used to plot lines. These patterns are very often extremely beautiful and always ‘self-repeating’ – i.e. however small a piece of the pattern we look at, we will find the same pattern repeating itself in a smaller size within it.
When a very small part of such an equation is changed – the resulting change in a pattern is usually enormous and unpredictable – and we have ‘The Butterfly Effect’ – where the small flapping of butterfly wings in one part of the world is said to influence the weather elsewhere perhaps days or weeks afterward.
So, by creating equations which attempt to simulate something like the weather we often end up with fractal patterns. And this of course is where the problem lies. The weather is influenced by many changing things – and by the time we have achieved a good set of equations for it, something will have changed, and the ensuing result will be a dramatically different fractal.
So what would be the point of doing this anyway? Well, many mathematicians believe that it might be possible to come up with a set of equations which are sufficiently accurate but which also do not dramatically change with just any small change to their set up. In this way we could predict something like the weather without getting it wrong so often.
See if you can google ‘fractals’ and you will easily find many examples of these patterns. In fact there are also sites which allow you to create your own fractal and even use it to play music!
