Simple R implementation of cellular automata described in A New Kind of Science.

newkindofscience.r

# A few simple rules from Stephen Wolfram's A New Kind of Science

apply_rule <- function(x, rule = "254") {
  stopifnot(length(x) == 3)
  stopifnot(all(x %in% c(0, 1)))
  
  rules <- list("254" = c(1, 1, 1, 1, 1, 1, 1, 0),
                "250" = c(1, 1, 1, 1, 1, 0, 1, 0),
                "90"  = c(0, 1, 0, 1, 1, 0, 1, 0),
                "30"  = c(0, 0, 0, 1, 1, 1, 1, 0))
   
  rule <- setNames(rules[[rule]], 
                   c("111", "110", "101", "100", "011", "010", "001", "000"))
                

  rule[paste(x, collapse = "")]
}



ncols <- 500
rule <- "30"

x <- matrix(0, ncol = ncols + 1, nrow = ncols / 2)
x[1, ncols / 2 + 1] <- 1

for (i in 1:nrow(x)) {
  if (i == nrow(x)) break
  newrow <- mapply(function(j1, j2) apply_rule(x[i, j1:j2], rule), 
                       j1 = 1:(ncol(x) - 2), j2 = 3:ncol(x))
  x[i + 1,] <- c(0, newrow, 0)
}


image(t(x)[, nrow(x):1], col = c("white", "black"), axes = FALSE)
grid(ncol(x), nrow(x), lty = 1)
box(col = "lightgray")