animation (version 1.1-0)

quincunx: Demonstration of the Quincunx (Bean Machine/Galton Box)

Description

This function simulates the quincunx with ``balls'' (beans) falling through several layers (denoted by triangles) and the distribution of the final locations at which the balls hit is denoted by a histogram.

Usage

quincunx(balls = 200, layers = 15, pch.layers = 2, pch.balls = 19, 
    col.balls = sample(colors(), balls, TRUE), cex.balls = 2)

Arguments

balls

number of balls

layers

number of layers

pch.layers

point character of layers; triangles (pch = 2) are recommended

pch.balls, col.balls, cex.balls

point character, colors and magnification of balls

Value

• A named vector: the frequency table for the locations of the balls. Note the names of the vector are the locations: 1.5, 2.5, ..., layers - 0.5.

Details

The bean machine, also known as the quincunx or Galton box, is a device invented by Sir Francis Galton to demonstrate the law of error and the normal distribution. When a ball falls through a layer, it can either go to the right or left side with the probability 0.5. At last the location of all the balls will show us the bell-shaped distribution.

References

http://en.wikipedia.org/wiki/Bean_machine http://animation.yihui.name/prob:bean_machine

See Also

rbinom

Examples

set.seed(123)
ani.options(nmax = 200 + 15 -2, interval = 0.03)
freq = quincunx(balls = 200, col.balls = rainbow(200))
# frequency table
barplot(freq, space = 0)

ani.options(ani.height = 500, ani.width = 600, 
    interval = 0.03, nmax = 213, title = "Demonstration of the Galton Box", 
    description = "Balls falling through pins will show you the Normal
    distribution.")
ani.start()
quincunx()
ani.stop()