Demonstration of the Quincunx (Bean Machine/Galton Box)

Description

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; quincunx() is shows single layer, and quincunx2() is a two-stage version of the quincunx.

Usage

quincunx2(balls = 200, layers = 15, pch.layers = 2, pch.balls = 19, 
    col.balls = sample(colors(), balls, TRUE), cex.balls = 2)

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

Arguments

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.

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.

Note

The maximum number of animation frames is controlled by ani.options('nmax') as usual, but it is strongly recommended that ani.options(nmax = balls + layers -2), in which case all the balls will just fall through all the layers and there will be no redundant animation frames.

Author(s)

Yihui Xie, Lijia Yu, and Keith ORourke

References

http://vis.supstat.com/2013/04/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 = paste("'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)
set.seed(123)
oopt = ani.options(nmax = ifelse(interactive(), 200 + 15 - 
    2, 2), interval = 0.03)
freq = quincunx2(balls = 200, col.balls = rainbow(200))

## frequency table
barplot(freq$top, space = 0)  # top layers
barplot(freq$bottom, space = 0)  # bottom layers

## HTML animation page
saveHTML({
    ani.options(nmax = ifelse(interactive(), 200 + 15 - 
        2, 2), interval = 0.03)
    quincunx2(balls = 200, col.balls = rainbow(200))
}, img.name = "quincunx2", htmlfile = "quincunx2.html", 
    ani.height = 500, ani.width = 600, single.opts = paste("'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)