A demonstration of a 2-D Brownian motion:

set.seed(123)
x = rnorm(5)
y = rnorm(5)
for (i in 1:100) {
    plot(x <- x + 0.1 * rnorm(5), y <- y + 0.1 * rnorm(5), xlim = c(-3, 3), 
        ylim = c(-3, 3), col = "steelblue", pch = 16, cex = 2, xlab = "x", ylab = "y")
}