The R Book

Temporal and Spatial Dynamics: a Simulated Random Walk in Two Dimensions

The idea is to follow an individual as it staggers its way around a two-dimensional random walk, starting at the point (50, 50) and leaving a trail of lines on a square surface which scales from 0 to 100. First, we need to define what we mean by our random walk. Suppose that in the x direction the individual could move one step to the left in a given time period, stay exactly where it is for the whole time period, or move one step to the right. We need to specify the probabilities of these three outcomes. Likewise, in the y direction the individual could move one step up in a given time period, stay exactly where it is for the whole time period, or move one step down. Again, we need to specify probabilities. In R, the three movement options are c(1,0,-1) for each of the types of motion (left, stay or right, and up, stay or down) and we might as well say that each of the three motions is equally likely. We need to select one of the three motions at random independently for the x and y directions at each time period. In R we use the sample function for this:

sample(c(1,0,-1),1)

which selects one value (the last argument is 1) with equal probability from the three listed options (+1, 0 or −1). Out of 99 repeats of this procedure, we should expect an average of 33 ups and 33 downs, 33 lefts and 33 rights.

We begin by defining the axes and drawing the start position in red:

plot(0:100,0:100,type="n",xlab="",ylab="") ...