My probability teacher opened our class of Markov Chain Model by giving us the drunk man hypothesis - A drunk man will find his way home. We all had a laugh, but I had an urge to try this out everytime I was in those shoes. What better way to simulate this experiment.

Link to fiddle - Link to fiddle - http://jsfiddle.net/27thmartian/y16sqcb0/embedded/result/

Visualisation Notes:

• Walker starts from origin to walk randomly in unit steps
• We need to see if walker will come back to origin
• A random generator decides whether the person goes north-south or west-east.
• A Second randomizer moves walker to forward or backward in the previously selected dimension.
• The chart is re-rendered after the given amount of time, defaulted to 50 ms.
• A walker may or maynot hit the origin. Increase the steps to see if it returns to origin
• At the end of the program, we see the Average Steps taken to Return to Origin

Assumptions

• Each step takes 1 unit time
• Walker takes one of the equally likely four paths available - North, South, East or West
• Each change in direction is exactly at right angles

Conclusion

If you let walker walk long enough it will come back to origin

or a drunk person - who can follow the easy assumptions of -

• walking exact size steps
• turning at exact right angles will eventually reach home