StarLogo Project:

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 to 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.)