n <- 10
dirs <- sample(c("L","R","S"), n-1, replace=T)

## Initial position
pos <- c(1, 0)

## Initial displacement
displ <- c(1,0)


## Begin the plot
plot(NULL,type=NULL,xlim=c(-n,n),ylim=c(-n,n),xlab='x',ylab='y')
myColors <- palette(rainbow(n))

## Initialize path to contain the first segment
path <- cbind(pos)

## Plot initial position
points(pos[1], pos[2], col=myColors[0],pch=19)


for(i in 1:length(dirs)) {
  dir <- dirs[i];

  ## Compute new displacement
  if( all.equal(displ, c(1,0)) == TRUE) {
    if (dir == "L")
      {
        displ <- c(0,1)
      }
    else if(dir=="R")
      {
        displ <- c(0,-1)
      }
  }
  else if( all.equal(displ, c(0,1)) == TRUE) {
    if (dir == "L")
      {
        displ <- c(-1,0)
      }
    else if(dir=="R")
      {
        displ <- c(1,0)
      }
  }
  else if( all.equal(displ, c(-1,0)) == TRUE) {
    if (dir == "L")
      {
        displ <- c(0,-1)
      }
    else if(dir=="R")
      {
        displ <- c(0,1)
      }
  }
  else if( all.equal(displ, c(0,-1)) == TRUE) {
    if (dir == "L")
      {
        displ <- c(1,0)
      }
    else if(dir=="R")
      {
        displ <- c(-1,0)
      }
  }


  ## Add new displacement to position
  pos <- pos + displ
  path <- cbind(path, pos)

  ## Plot current position in the i-th color
  points(pos[1], pos[2], col=myColors[i], pch=19)
}

## Plot the path
lines(t(path),type="l",lwd=2,col="magenta")

#grid(nx=2*n, ny=2*n)
## Draw grid manually
for (x in -n:n)   lines(c(x,x),c(-n,n), col="gray",lty=2)
for (y in -n:n)   lines(c(-n,n),c(y,y), col="gray",lty=2)