This models a simple one dimensional random walk, showing that the average absolute distance from the initial position converges to a square root function. This is interesting due to the (non-absolute) average of the distances is near zero.
To run the model, click "setup" then "go". The model ends when a turtle reaches the maximum distance right or left. The "scale" slider specifies how many steps each "patch" is. At "1", the stopping distance is 100, at "5" it is 500.
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view/download model file: walk.nlogo