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Issue 5.2



Random Walks

Issue: 5.2 (January/February 2007)
Author: JC Cruz
Author Bio: JC is a freelance engineering consultant currently residing in British Columbia. He develops custom OS X applications and teaches origami at the local district libraries. He can be reached at: anarakisware@cashette.com
Article Description: No description available.
Article Length (in bytes): 36,198
Starting Page Number: 17
Article Number: 5209
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Download Icon 5209.zip Updated: 2013-03-11 19:07:59

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Excerpt of article text...

This article explores the concept of a random walk model and some of the basic mathematics behind it. It will also demonstrate how to use REALbasic to simulate a random walk occurring in one and two dimensions.


In previous articles, ordinary differential equation (ODE) algorithms were used to simulate the motion of various physical systems. Furthermore, these simulated systems behave consistently and in accordance to the three Laws of Motion stated by Isaac Newton. Because of their predictable nature in the physical world, they are often referred to as deterministic systems.

However, there are certain systems whose behaviors are difficult, if not impossible, to simulate by conventional means. They display movement so complex that it appears to be totally random. Such complexity is usually caused by large numbers of near instantaneous interactions between the objects in the system. This is especially true when the dimensions of said objects approach molecular levels.

These complex systems are known as non-deterministic or stochastic systems. Simulating them using Newtonian laws and ODE algorithms requires considerable amounts of dedicated computational power. A simpler and more effective approach, however, is to approximate these systems as random walk models.

The Nature of Random Walks

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