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.

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

In