quincunx | R Documentation |
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.
quincunx(
balls = 200,
layers = 15,
pch.layers = 2,
pch.balls = 19,
col.balls = sample(colors(), balls, TRUE),
cex.balls = 2
)
quincunx2(
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.balls, col.balls, cex.balls |
point character, colors and magnification of balls |
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.
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, Lijia Yu, and Keith ORourke
Examples at https://yihui.org/animation/example/quincunx/
rbinom
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