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Galton's Box

The Galton box is an experimental device that is made of a board in which needles are disposed in a quincunx pattern and under which cylindrical cups are disposed. When one drops balls on the top of the board, each time the ball collide a needle, it has a chance over two to choose the left side of the needle or the right side of the needle.

If one drop a sufficiently large amount of balls, the figure made by the balls in the cup is bell-shaped, illustrating the convergence of the ball distribution to the Normal distribution.

See http://en.wikipedia.org/wiki/Bean_machine for further information.

Why this logo for OpenTURNS?

Galton's experiment is very representative of OpenTURNS goal: based on a deterministic device (the board) feeded-up by random input (the balls initial position), obtain statistical informations about the experiment outcome (the distribution of the balls in the cups).

How this logo has been created?

This logo is the result of an effective physically-based numerical simulation of a virtual Galton box, in which the initial horizontal position of the balls follow a uniform distribution tightly centered about the position of the top needle.

The physical behaviour of the Galton box has been simulated using the Open Dynamic Engine library. It takes into account collisions, friction and gravity.

This simulation has been used as an input for a 3-D rendering using Persistenc Of Vision Ray-Tracer. The cups are made of tainted glass, the needles have a copper finish and the board is covered with a green velvet.

The resulting animation has been post-processed using ImageMagick.

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Last modified 8 years ago Last modified on 07/21/09 11:42:19

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