quincunx {animation} | R Documentation |
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. 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.
quincunx(balls = 200, layers = 15, pch.layers = 2, pch.balls = 19, col.balls = sample(colors(), balls, TRUE), cex.balls = 2)
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 |
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.
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.
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.
Yihui Xie
http://en.wikipedia.org/wiki/Bean_machine
http://animation.yihui.name/prob:bean_machine
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) ## Not run: ani.options(ani.height = 500, ani.width = 600, outdir = getwd(), 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() ## End(Not run)