RANDOM WALK

Normal distribution

The concept

There is one remarkable thing about randomness: Its existence is neither proved nor disproved it even appears everyday in science and in our everyday lives. Random walk is interesting for people who want to know more about the mystic character of this invisible companion.

This diploma thesis was created at the University of Applied Sciences in Mainz, Germany by Daniel A. Becker in 2009 and was supervised by Prof. Johannes Bergerhausen.

The visualizations

All visualizations of physical mathematical phenomena are not just illustrated representations; they are actually simulated with the help of „proce55ing“. True chaos and order within randomness has been demonstrated by the use of pure numerical data and software simulations. Therefore, the software not only presents the visualizations but it also uses the graphics to prove the phenomenon of randomness.

Normal distribution

Physical experiments are also subject to mathematical probabilities. The bean machine, also known as the Galton Box, clearly shows normal distribution in action. The machine consists of a vertical board with interleaved rows of pins. A ball is dropped from the top and on its way down it bounces left and right until it leaves the machine at the bottom. The path of any single ball cannot be predicted; however, the number of balls in each row when all rows are taken together, approximates a bell curve.

The most heavily colored areas within the visualization depict those parts of the machine which were passed through more often: Mainly the direct way down.

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