typX <- function() {
  M <- matrix(rep(0,100),10)
  M[1:2,1:2] <- 1
  M[1:2,8:9] <- 1
  M[3:6,4:6] <- 1
  M[6,1]
  M[6,9]
  M[7,1:2] <- 1 
  M[7,8:9] <- 1 
  M[8,2:4] <- 1 
  M[8,6:8] <- 1 
  M[9,3:7] <- 1
  A <- matrix(c((runif(1)+3)/6,0,0,(runif(1)+1)/3),2)
  winkel <- runif(1)*2*pi
  B <- matrix(c(cos(winkel),sin(winkel),-sin(winkel),cos(winkel)),2)%*%A
  U <- matrix(rep(0,100),10)
  for(i in 1:10)
    for(j in 1:10) {
      x <- round(c(5.5,5.5) + B%*%(c(i,j)-5.5))
      U[x[1],x[2]] <- M[i,j]
    }
  U[2:9,2:9]
}

typY <- function() {
  M <- matrix(rep(0,100),10)
  x <- sample(1:9,1)
  y <- sample(1:9,1)
  M[x:(x+1),y:(y+1)] <- 1
  x <- sample(1:9,1)
  y <- sample(1:9,1)
  M[x:(x+1),y:(y+1)] <- 1
  x <- sample(1:7,1)
  y <- sample(1:8,1)
  M[x:(x+3),y:(y+2)] <- 1
  x <- sample(1:10,1)
  y <- sample(1:10,1)
  M[x,y] <- 1
  x <- sample(1:10,1)
  y <- sample(1:10,1)
  M[x,y] <- 1
  x <- sample(1:10,1)
  y <- sample(1:9,1)
  M[x,y:(y+1)] <- 1
  x <- sample(1:10,1)
  y <- sample(1:9,1)
  M[x,y:(y+1)] <- 1
  x <- sample(1:10,1)
  y <- sample(1:8,1)
  M[x,y:(y+2)] <- 1
  x <- sample(1:10,1)
  y <- sample(1:8,1)
  M[x,y:(y+2)] <- 1
  M[9,3:7] <- 1
  A <- matrix(c((runif(1)+3)/6,0,0,(runif(1)+1)/3),2)
  winkel <- runif(1)*2*pi
  B <- matrix(c(cos(winkel),sin(winkel),-sin(winkel),cos(winkel)),2)%*%A
  U <- matrix(rep(0,100),10)
  for(i in 1:10)
    for(j in 1:10) {
      x <- round(c(5.5,5.5) + B%*%(c(i,j)-5.5))
      U[x[1],x[2]] <- M[i,j]
    }
  U[2:9,2:9]
}

image(typX())
image(typY())