Gaussian
What is it?
This project simulates a classic science-museum exhibit in which balls are dropped through a triangular bed of nails. When a ball hits a nail, it probabilistically shifts either to the left or to the right. At the bottom of the nails, the balls form a Gaussian distribution.
How to Use It
Click the `setup` button to setup the triangular array of nails. Click the `go` button to start the balls dropping through the nails. The `depth` slider controls the depth of the triangular array of nails. There is a "bar" at the bottom of the screen to stop the balls from falling. Click the `remove-bar` button to remove the bar. The balls will continue to fall, "wrapping" back to the top of the screen and falling through the array of nails again. Click `add-bar` to re-insert the bar at the bottom of the screen. |
Things to Notice
When a ball hits a nail, it has a 50% chance of shifting to the left and a 50% chance of shifting to the right. So each ball is doing a horizontal random walk (while falling downward). The depth of the triangular array of nails sets the number of steps in the random walk. The resulting Gaussian distribution is typical of a random walk. When you remove the bar at the bottom of the screen (by clicking the `remove-bar` button), the balls "wrap" and fall through the nails again. So each point in the original Gaussian distribution becomes a mini-Gaussian distribution. The overall distribution is the sum of these mini-Gaussian distributions.
Explorations
Change the `fall` program so that balls are biased to shift to the left when they hit nails (perhaps going to the left 75% of the time). What is the effect on the resulting distribution?
StarLogo Features
The `setup-triangle` procedure uses a special type of "turtle recursion." When a turtle runs the procedure, it hatches two new turtles, each of which runs `setup-triangle`. The original turtle then dies. The current depth of the recursion is kept as a local state variable in the turtles. The `new-ball` procedure creates a new ball and places it at the top of the screen. There is a button that runs the `new-ball` procedure every 0.2 seconds. An alternate approach: Place one turtle at the top of the screen and make it continually `hatch` new turtles. (But you must make sure that the "hatching" turtle doesn't fall like the other turtles.)
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