Chaos & Ordnung - IAAC

If you want to measure the length of a fractal, you will
see that this length is endless. We did an experiment,
where we tried to measure some kind of fractal with
different scales. The smaller the scales got the length
of the fractal got bigger and bigger. If you would
choose the scale to be endless small, the length of the
fractal would get endless. If you look at coasts as
fractals you can say, that every coast in the world is
as long as another- endless.( if you watch the coast
from the satellite you can measure some length. If you
come closer you will see that there are some small
bays- if you measure now, the coast is longer. If you
go to these bays, you will see that there are some
rocks- the coast gets longer. But the rocks are not
smooth.......).
If you try to calculate a fractal, there are always some
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.
Fractals also have their own dimensions. If the fractal is
in 2 dimensional space its form is something between a
line and a square and so its fractal dimension is between
1 and 2. If the fractal is in 3 dimensional space, its form
is something between a square and a cube, so its
dimension is between 2 and 3.
Another important point are dynamic systems. So what
is a dynamic system? An 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
reduce 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.
In a linear system you get a value of y for every x you
choose. The form of the function is predictable. If you
have a non- linear system, the values are not predictable.
In the beginning the function might be growing and
then suddenly start to move between two or more pints.
It is like broken lines. The function is depending on one
constant value. It might look completely different if the
factor is between 0 an 1, 1 and 3 or if it is larger than 3.
In nature we can find fractals almost everywhere, but
they are not built strictly after mathematical rules. Almost
every object can be described by fractals.
Nature brings out fractals in all shapes and sizes. In
each plant there is one pattern that repeats itself over
and over. In nature it is not endless because of physical
rules (gravity, weight...). In nature the patterns of fractals
are never exactly the same, there are little differences
(colour, size...). Nature regenerates its patterns when
they are destroyed by outer forces (e.g.: if a branch
brakes there will grow at least two new branches at the
same place).
When we look at nature today we just see the moment.
We cannot see how plants looked like some million
years ago and we cannot forecast 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.
We also heard about the chaos theory. One example is
the butterfly- effect. It says that if a butterfly in South
Africa spreads its wings it might cause a tornado in
Texas. That is a thing you also cannot predict.
17