# Exercise Sheet 7 - Exercise 2c

d <- 8                                   # window size
entries <- rep(0,d*d)                    # initialize entries of window
cm <- array(entries, dim=c(d,d))         # initialize the window
n <- 1000                                # set number n
k <- 1000                                # set number k
lambda <- 1                              # set lambda
numvert <- rep(0,n)                      # counts the number of vertices having value 1
for (i in 1:k) {
   print(i)
   for (j in 1:n) {
      posx <- round(runif(1,0.5,d + 0.5))  # choose x-coordinate uniformly
      posy <- round(runif(1,0.5,d + 0.5))  # choose y-coordinate uniformly
      u <- runif(1)                        # uniform random number u
      # now check the values of the neighboring points and update if u < lambda/(lambda+1) and no neighbouring point equals 1
      if ((cm[max(posx-1,1),posy] == 0) & (cm[min(posx+1,d),posy] == 0) & (cm[posx,max(posy-1,1)] == 0) & (cm[posx,min(posy+1,d)] == 0) &
          (cm[max(posx-1,1),max(posy-1,1)] == 0) & (cm[max(posx-1,1),min(posy+1,d)] == 0) & (cm[min(posx+1,d),max(posy-1,1)] == 0) & (cm[min(posx+1,d),min(posy+1,d)] == 0) & (u < lambda/(lambda+1))) {
         cm[posx,posy] <- 1
      } else {
         cm[posx,posy] <- 0
      }
   }
   numvert[i] <- sum(cm)                   # save number of vertices having value 1 after every n-th step
}
meanvalue <- mean(numvert)                 # calculates the mean number of vertices having value 1