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
quincunx2() is a two-stage version of the quincunx.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
number of balls
number of layers
point character of layers; triangles (
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
Yihui Xie, Lijia Yu, and Keith ORourke
Examples at https://yihui.org/animation/example/quincunx/
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