Brownian Motion

The function brownian.motion() has illustrated the phenomenon of Random Walk on the 2D plane. For a point (x, y), its next location is (x + rnorm(1), y + rnorm(1)).

library(animation)
saveHTML({
    ani.options(interval = 0.05, nmax = 100)
    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)
    brownian.motion(pch = 21, cex = 5, col = "red", bg = "yellow")
}, img.name = "brownian_motion", htmlfile = "brownian_motion.html", 
    ani.width = 500, ani.height = 500, 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)."))
	

The animation is like this:

Random walk on the 2D plane: for each point (x, y), x = x + rnorm(1) and y = y + rnorm(1). </ani>

• I find this Java applet is much more interesting than my function: Einstein's Explanation of Brownian Motion

If you use the lattice package, don't forget to print() your plots, otherwise graphics devices like png() will not be able to record your images. Here is an example:

library(animation)
library(lattice)
saveHTML({(bm.mat = data.frame(x = rnorm(10), y = rnorm(10)))
    ani.options(interval = 0.05, nmax = 100,)
	## Brownian Motion in lattice
	for (i in 1:ani.options("nmax")) {
    print(xyplot(y ~ x, bm.mat, xlim = c(-10, 10), ylim = c(-10, 10), pch = 19))
    bm.mat = bm.mat + data.frame(x = rnorm(10), y = rnorm(10))
	}},img.name="Brownian_Motion", hltmfile="Brownian_Motion.html",
	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)."))