====== Brownian Motion ======
The function ''brownian.motion()'' has illustrated the phenomenon of [[wp>random_walk|Random Walk]] on the 2D plane. For a point ''(x, y)'', its next location is ''(x + rnorm(1), y + rnorm(1))''.
===== R code =====
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)."))
===== Animation =====
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).
===== Other resources =====
* I find this Java applet is much more interesting than my function: [[http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/brownian/brownian.html|Einstein's Explanation of Brownian Motion]]
===== Reminder to lattice users =====
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)."))