This is an interactive visualization of simple random walks.
 
Use the left and right arrow buttons to change the speed. Press "2" or "3" to toggle between +1/-1 and +1/0/-1 random walks. Press "r" to restart. Press "c" or the space bar to toggle between single view where you'll see one random walk at a time and cumulative view where you'll see a succession of random walks.
 
In cumulative view, the curve at the bottom shows the average vertical distance from the starting point, scaled by a factor of two. (The orange curve is what this average should converge to according to the central limit theorem.) Press "d" in single view to see the standard deviation in orange.
 
[Should work with recent desktop versions of Chrome or Firefox.]
 

 
Copyright (c) 2016, Prof. Dr. Edmund Weitz.