# RANDOM WALK

#### The number Pi

#### 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.

#### The random walk of PI

The constant number pi has an infinite number of decimal places with no recognizable system within the sequence. However, the distribution of the 10 possible digits is quite uniformly balanced – at least within the displayed range from 1 to 1,000,000 positions after the comma. Each digit is represented by a direction from 0° to 360°. For example, each time the 0 arises, a line with a certain fixed length is displayed with the value of 0°. The end of each line is at the same time the start of the line for the following digit; the length of each line remaining constant. The result of the lines is a path; the so called random walk.

The colored areas represent the distribution of the decimal of pi. These always start with 0, but with each succeeding step the values are increased by 10,000. These areas are laid around the most extreme points of the random walk. It can be observe that the lager the displayed range becomes the more round the areas are.