#prorgamming

What is a Random Walk?

A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers. An elementary example of a random walk is the random walk on the integer number line, which starts at 0 and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be approximated by random walk models, even though they may not be truly random in reality. As illustrated by those examples, random walks have applications to many scientific fields including ecology, psychology, computer science, physics, chemistry, biology as well as economics. Random walks explain the observed behaviors of many processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity. As a more mathematical application, the value of pi can be approximated by the usage of random walk in agent-based modelling environment. The term random walk was first introduced by Karl Pearson in 1905 (source Wikipedia, For More Info : Random Walker – Wikipedia).

The Code

The code contains a single function that displays the walker on 2-D surface. at each step, the direction of walker changes to any 4 of the directions (up, down, left, right). The complete path of walker is traced from beginning and the number of steps taken is displayed at the top bar. The program also saves photo of the pattern at 1,000, 10,000, 50,000, 100,000, 500,000 steps.

Code to Random Walker : Random Walker

Time Lapse Video : Random Walker – Time Lapse

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Further Developments

In the next post (and video on YouTube) there will be some of the Random Walk applications . Stay tuned!

  Your thoughts and suggestions will be much appreciated!

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