# quincunx: Demonstration of the Quincunx (Bean Machine/Galton Box) In animation: A Gallery of Animations in Statistics and Utilities to Create Animations

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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 ) ```

## 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

## 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

`rbinom`