mat.example.list = list(matrix(c(1,1,1,1,0, 0,0,0,1,0, 1,1,1,1,0, 0,1,0,0,0, 0,1,1,1,1), 5, 5),
                        matrix(c(1,1,1,1,0, 0,0,0,1,0, 0,1,1,1,0, 0,1,0,0,0, 0,1,1,1,1), 5, 5),
                        matrix(c(1,1,1,1,0, 0,0,0,1,0, 0,1,1,0,0, 0,1,0,0,0, 0,1,1,1,1), 5, 5))

percolate.board = function(mat) {
  assert_that(is.valid(mat))
  assert_that(onlyZerosandOnes(mat))
  #top row of matrix with empty cells is filled with 'water'
  for (i in 1:ncol(mat)) {
    if (mat[1,i] == 1) mat[1,i] = 2
  }
  while (TRUE) {
    #check to see if the matrix changes at all
    oldMat = mat
    #keeps track of all the indices where a 1 appears
    onesIndex = list()
    #returns a matrix with TRUEs and FALSEs
    onesMatrix = (mat == 1)
    index = 1
    for (r in 1:nrow(onesMatrix)) {
      for (c in 1:ncol(onesMatrix)) {
        if (onesMatrix[r,c]) {
          onesIndex[[index]] = c(r,c)
          index = index + 1
        }
      }
    }
    if (length(onesIndex) == 0) break
    #loop over the list containing the indices of the 1s
    for (i in 1:length(onesIndex)) {
      row = onesIndex[[i]][1]
      col = onesIndex[[i]][2]
      left = col - 1
      right = col + 1
      top = row - 1
      bottom = row + 1

      if (1 <= left & left <= ncol(mat)) {
        if (mat[row, left] == 2) mat[row, col] = 2
      }
      if (1 <= right & right <= ncol(mat)) {
        if (mat[row, right] == 2) mat[row, col] = 2
      }
      if (1 <= top & top <= nrow(mat)) {
        if (mat[top, col] == 2) mat[row, col] = 2
      }
      if (1 <= bottom & bottom <= nrow(mat)) {
        if (mat[bottom, col] == 2) mat[row, col] = 2
      }
    }

    if (all(mat == oldMat)) break
  }
  result = FALSE
  #check if matrix percolated or not
  for (i in 1:ncol(mat)) {
    if (mat[nrow(mat),i] == 2) result = TRUE
  }

  return(list(result.mat = mat, result = result))
}

par(mfrow = c(2,3))

for (i in 1:3) {
  plot.board(mat.example.list[[i]])
  plot.board(percolate.board(mat.example.list[[i]])[["result.mat"]])
}