Chaos & Ordnung - IAAC

Something about Chaos (physics group)
What we have learned about chaos in our during the week
At the beginning we thought, that chaos and order are two different things and that the word could be described
by order. Now we are aware that ...
Many people would define the chaos simply as a system where there is no order. But chaos is much more
than no order because in every system even, if it doesn’t look so, you can find some rules. And this rules are
the most important things in a system to find out because then you can see that every chaotic system is in
reality no chaos but a very strangely ordered system which appears a little bit abnormal - unclear.
So in general you can say that every system has its rules which define the look-like of the system, the macroscopic
behaviour of the system. These rules could be different from system to system. So we could say
that everything that exists on Earth is a system by itself and at the same time it is in contact with other system,
influencing each other in some way. The systems consist of many subsystems influenced by force fields
in which they are located - these can be outer fields or such fields which they create by self-organisation. In
the system there can occur many random events.
We think that some things are the same, but in reality you cannot say that some thing is exactly like an other
because everything develops in a different direction and are in different conditions. So we can say that our
whole Universe is a big order of nature but for us human beings it is confusing chaos.
There is no chaos and order but one Nature. Chaos relates to us and we must try to keep realistic and practical
and try to understand it as a wonderful unique miracle. Our challenge is to find our order. It relates to us
to accept the chaos.
The concepts of chaos and order are always related to a concrete system:
PENDULUMS
Considering about pendulums we usually think about simple mechanical
systems. A mathematical pendulum is used as a classic
example of regular periodic motion. Real pendulums do not act as
mathematical pendulums. They either loose energy and stop in a
certain time or they behave in chaotic way. A good example of chaotic
motion is the magnetic pendulum. We could use it also as a
model for complex chaotic systems of Nature (the beating of our
heart, breathing, raining, lightning, population of animals, fluctuations
of radio signals, and in the electric net, etc). The common features of
these systems are:
• DYNAMICS – the stage of the system is in development, it undergoes
permanent changes until it is not interrupted or stopped.
• UNSTABLE REGIONS - the chaotic system gets many times
through unstable regions. These are the regions where the system must decide between different possibilities
of its development.
• INITIAL CONDITIONS – the chaotic system is strongly influenced by the initial conditions. We can never
repeat them exactly in the same way. The system is always in different constellation, starting with different
amount of energy etc.
The conditions can be also influenced during the development!
• ATTRACTORS – in spite of the differences of development the system is attracted to/or round significant
stages.
SAND
Sand is an example of a SYSTEM OF MANY PARTICLES. This means that particles influence each other
and all the particles together behave as one non-linear system. We cannot say what will happen with a certain
grain of sand, we can only make predictions about some features of the system as a whole – about the
main values of its characteristics. But the characteristics of each grain – their shapes, volumes, weights of
course influence them.
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