animation (version 2.0-5)

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

## HTML animation page
saveHTML({
    ani.options(nmax = ifelse(interactive(), 200 + 15 - 2, 2), 
        interval = 0.03)
    quincunx(balls = 200, col.balls = rainbow(200))
}, img.name = "quincunx", htmlfile = "quincunx.html", ani.height = 500, 
    ani.width = 600, single.opts = "'controls': ['first', 'previous', 'play', 'next', 'last', 'loop', 'speed'], 'delayMin': 0", 
    title = "Demonstration of the Galton Box", description = c("Balls", 
        "falling through pins will show you the Normal", "distribution."))

ani.options(oopt)