Demonstration of Brownian motion on the 2D plane

Description

Brownian motion, or random walk, can be regarded as the trace of some cumulative normal random numbers.

Usage

brownian.motion(n = 10, xlim = c(-20, 20), ylim = c(-20, 20), ...)

Arguments

Details

The location of the next step is “current location + random Gaussian numbers”, i.e.,

x[k + 1] = x[k] + rnorm(1)

y[k + 1] = y[k] + rnorm(1)

where (x, y) stands for the location of a point.

Value

None (invisible NULL).

Note

The maximum number of steps in the motion is specified in ani.options('nmax').

Author(s)

Yihui Xie <http://yihui.name>

References

http://vis.supstat.com/2012/11/brownian-motion-with-r

See Also

rnorm

Examples

oopt = ani.options(interval = 0.05, nmax = ifelse(interactive(), 150, 2))
brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow", main = "Demonstration of Brownian Motion")
ani.options(oopt)

## create an HTML animation page
saveHTML({
    par(mar = c(3, 3, 1, 0.5), mgp = c(2, 0.5, 0), tcl = -0.3, cex.axis = 0.8, cex.lab = 0.8, 
        cex.main = 1)
    ani.options(interval = 0.05, nmax = ifelse(interactive(), 150, 10))
    brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow")
}, single.opts = "'controls': ['first', 'previous', 'play', 'next', 'last', 'loop', 'speed'], 'delayMin': 0", 
    title = "Demonstration of Brownian Motion", description = c("Random walk on the 2D plane: for each point", 
        "(x, y), x = x + rnorm(1) and y = y + rnorm(1)."))

ani.options(oopt)