Chaos & Ordnung - IAAC

cast how they will look in the future. We can only predict how it is going to be, but nature will form as the
conditions in the future will be.
Chaos is something that is not predictable over a long time. That happens, because a dynamic system is
sensitive to initial conditions. The more unstable initial conditions a system has the more chaotic it is. You
can only predict something for a short time.
"In other words, it is unpredictable and yet contains regularity." ( by sci. fractals FAQ) In chaotic systems we
can find examples that show us that the little differences at the beginning of a process can be multiplied during
and cause big differences in the end.
Examples are:
The butterfly- effect: It says that if a butterfly in South Africa spreads its wings this effect can be increased
that much that it can cause a tornado in Texas.
The weather: There are a lot of unpredictable initial conditions that are changing all the time. Because of that
you can only forecast the weather for some days.
If you try to calculate chaotic events, there are always calculating mistakes. After each iteration the mistake
is multiplied. In the beginning it might be very small, but after some time it leads to chaos. But still there are
regions in this chaos where there is order.
Another example: You have little predators and a lot of prey, the number of predators will increase. But because
of that the number of prey will reduceà not enough food for the predators. Their number reduces. Now
the prey have the possibility to increase their number. It is a never ending circle.
Dynamical systems can be explained by linear and non- linear functions. The difference between linear and
non- linear functions is how the change of the function looks. In a linear function this change is - surprise-
linear. And in a non- linear function it does not have to be linear. So all that matters is how the change of the
function looks.
Expressing chaos through music
We found out that all things in nature can be expressed also by music. You can use sequences of DNA,
proteins, shapes of mountains... or you can just use algorithms to produce music. Tones can be connected
to parts of the sequences or with numbers in the algorithm. If you use a sequence to produce music it has
nothing to do with fractals, but if you use an algorithm you can say that you get fractal music. The principle is
the same as if you show the fractal on the monitor, but you are using tones instead.
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