animation (version 2.0-5)

brownian.motion: Demonstration of Brownian motion on the 2D plane

Description

Demonstration of Brownian motion on the 2D plane.

Usage

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

Arguments

n

Number of points in the scatterplot

xlim,ylim

Arguments passed to plot.default to control the apperance of the scatterplot (title, points, etc), see points for details.

...

other arguments passed to plot.default

Value

• None (invisible NULL).

Details

Brownian motion, or random walk, can be regarded as the trace of some cumulative normal random numbers: the location of the next step is just ``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.

References

http://animation.yihui.name/prob:brownian_motion

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)