w <- 256L
h <- 256L
set.seed(0)

lcg_prng <- function(n, y1, m, a, b) {
    if (n == 1) return(y1)
    res <- integer(n)
    res[1] <- y1
    for (i in 2:n) {
        y1 <- (a*y1 + b) %% m
        res[i] <- y1
    }
    res
}

m <- 2^11
z <- sample(1:m, w*h, replace=T)
img_sample <- matrix(z %% 2, nrow=w)

y <- lcg_prng(w*h, y1=1, m=m, a=1017, b=1)
img_lcg <- matrix(y %% 2, nrow=w)

par(mfrow=c(1,2), mar=c(1,1,1,1))
image(
  img_sample,
  col = c("black", "white"), 
  axes = FALSE,
  useRaster = TRUE, 
  asp=1, # fixes aspect ratio
  main="sample()") 
image(
  img_lcg,
  col = c("black", "white"), 
  axes = FALSE,
  useRaster = TRUE, 
  asp=1,
  main="lcg_prng()")