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| Mandelbrot Set |
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Brownian Motion
Brownian motion as described by Jean Perrin in 1909 is the motion of a particle that is acted
upon randomly by multiple forces. For collisions with a water molecule the effect is that the
particle will move in the opposite direction to the point of impact. The process of the particles
colliding with water molecules is random because the direction of the force of impact is
completely arbitrary. The result is a famous process called the "randomwalk". Interestingly,
the particles may appear random at first, but if they are watched for a sufficient amount of
time, the position may appear to average out in a central space because the forces causing the
particle to move may cancel each other out.
The idea that a particle experiencing chaotic motion whilst staying in a central position is a
mixture of a chaotic and deterministic phenomenon. This suggests that there is in fact a way of
controlling chaos using the ordered aspects of some chaotic systems. Large amounts of research
are being put into this idea. It may seem like a conflicting set of ideas, but quite often the
unpredictable sides of chaos can follow a pattern in some way. This applies to a surprisingly
large number of cases.
Next: How do you make a Fractal?
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