##### # #

## Go


### Sequential


```go
package main

import "fmt"

const (
    start    = "_###_##_#_#_#_#__#__"
    offLeft  = '_'
    offRight = '_'
    dead     = '_'
)

func main() {
    fmt.Println(start)
    g := newGenerator(start, offLeft, offRight, dead)
    for i := 0; i < 10; i++ {
        fmt.Println(g())
    }
}

func newGenerator(start string, offLeft, offRight, dead byte) func() string {
    g0 := string(offLeft) + start + string(offRight)
    g1 := []byte(g0)
    last := len(g0) - 1
    return func() string {
        for i := 1; i < last; i++ {
            switch l := g0[i-1]; {
            case l != g0[i+1]:
                g1[i] = g0[i]
            case g0[i] == dead:
                g1[i] = l
            default:
                g1[i] = dead
            }
        }
        g0 = string(g1)
        return g0[1:last]
    }
}

{{out}}

_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________

Concurrent

Computations run on each cell concurrently. Separate read and write phases. Single array of cells.

package main

import (
    "fmt"
    "sync"
)

const (
    start    = "_###_##_#_#_#_#__#__"
    offLeft  = '_'
    offRight = '_'
    dead     = '_'
)

func main() {
    fmt.Println(start)
    a := make([]byte, len(start)+2)
    a[0] = offLeft
    copy(a[1:], start)
    a[len(a)-1] = offRight
    var read, write sync.WaitGroup
    read.Add(len(start) + 1)
    for i := 1; i <= len(start); i++ {
        go cell(a[i-1:i+2], &read, &write)
    }
    for i := 0; i < 10; i++ {
        write.Add(len(start) + 1)
        read.Done()
        read.Wait()
        read.Add(len(start) + 1)
        write.Done()
        write.Wait()
        fmt.Println(string(a[1 : len(a)-1]))
    }
}

func cell(kernel []byte, read, write *sync.WaitGroup) {
    var next byte
    for {
        l, v, r := kernel[0], kernel[1], kernel[2]
        read.Done()
        switch {
        case l != r:
            next = v
        case v == dead:
            next = l
        default:
            next = dead
        }
        read.Wait()
        kernel[1] = next
        write.Done()
        write.Wait()
    }
}

Output is same as sequential version.

Groovy

Solution:

def life1D = { self ->
    def right = self[1..-1] + [false]
    def left = [false] + self[0..-2]
    [left, self, right].transpose().collect { hood -> hood.count { it } == 2 }
}

Test:

def cells = ('_###_##_#_#_#_#__#__' as List).collect { it == '#' }
println "Generation 0: ${cells.collect { g -> g ? '#' : '_' }.join()}"
(1..9).each {
    cells = life1D(cells)
    println "Generation ${it}: ${cells.collect { g -> g ? '#' : '_' }.join()}"
}

{{out}}

Generation 0: _###_##_#_#_#_#__#__
Generation 1: _#_#####_#_#_#______
Generation 2: __##___##_#_#_______
Generation 3: __##___###_#________
Generation 4: __##___#_##_________
Generation 5: __##____###_________
Generation 6: __##____#_#_________
Generation 7: __##_____#__________
Generation 8: __##________________
Generation 9: __##________________

Haskell

import System.Random (newStdGen, randomRs)
import Data.List (unfoldr)

bnd :: String -> Char
bnd bs =
  case bs of
    "_##" -> '#'
    "#_#" -> '#'
    "##_" -> '#'
    _ -> '_'

donxt :: String -> String
donxt xs =
  unfoldr
    (\xs ->
        case xs of
          [_, _] -> Nothing
          _ -> Just (bnd $ take 3 xs, drop 1 xs)) $
  '_' : xs ++ "_"

lahmahgaan :: String -> [String]
lahmahgaan xs =
  init .
  until ((==) . last <*> (last . init)) ((++) <*> (return . donxt . last)) $
  [xs, donxt xs]

main :: IO ()
main = do
  g <- newStdGen
  let oersoep = map ("_#" !!) . take 36 $ randomRs (0, 1) g
  mapM_ print . lahmahgaan $ oersoep

{{Out}}

*Life1D> mapM_ print . lahmahgaan $ "_###_##_#_#_#_#__#__"
"_###_##_#_#_#_#__#__"
"_#_#####_#_#_#______"
"__##___##_#_#_______"
"__##___###_#________"
"__##___#_##_________"
"__##____###_________"
"__##____#_#_________"
"__##_____#__________"
"__##________________"

*Life1D> main
"__##_##__#____###__#__#_______#_#_##"
"__#####_______#_#______________#_###"
"__#___#________#________________##_#"
"________________________________###_"
"________________________________#_#_"
"_________________________________#__"
"____________________________________"

=={{header|Icon}} and {{header|Unicon}}==

# One dimensional Cellular automaton
record Automaton(size, cells)

procedure make_automaton (size, items)
  automaton := Automaton (size, items)
  while (*items < size) do push (automaton.cells, 0)
  return automaton
end

procedure automaton_display (automaton)
  every (write ! automaton.cells)
end

procedure automaton_evolve (automaton)
  revised := make_automaton (automaton.size, [])
  # do the left-most cell
  if ((automaton.cells[1] + automaton.cells[2]) = 2) then
    revised.cells[1] := 1
  # do the right-most cell
  if ((automaton.cells[automaton.size] + automaton.cells[automaton.size-1]) = 2) then
    revised.cells[revised.size] := 1
  # do the intermediate cells
  every (i := 2 to (automaton.size-1)) do {
    if ((automaton.cells[i-1] + automaton.cells[i] + automaton.cells[i+1]) = 2) then
      revised.cells[i] := 1
  }
  return revised
end

procedure main ()
  automaton := make_automaton (20, [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0])
  every (1 to 10) do { # generations
    automaton_display (automaton)
    automaton := automaton_evolve (automaton)
  }
end

An alternative approach is to represent the automaton as a string. The following solution takes advantage of the implicit type coercions between string and numeric values in Icon and Unicon. It also surrounds the automaton with a border of 'dead' (always 0) cells to eliminate the need to special case the first and last cells in the automaton. Although the main procedure displays up to the first 10 generations, the evolve procedure fails if a new generation is unchanged from the previous, stopping the generation cycle early.

procedure main(A)
  A := if *A = 0 then ["01110110101010100100"]
  CA := show("0"||A[1]||"0")        # add always dead border cells
  every CA := show(|evolve(CA)\10)  # limit to max of 10 generations
end

procedure show(ca)
  write(ca[2:-1])                   # omit border cells
  return ca
end

procedure evolve(CA)
  newCA := repl("0",*CA)
  every newCA[i := 2 to (*CA-1)] := (CA[i-1]+CA[i]+CA[i+1] = 2, "1")
  return CA ~== newCA               # fail if no change
end

{{out|A couple of sample runs}}

->odca
01110110101010100100
01011111010101000000
00110001101010000000
00110001110100000000
00110001011000000000
00110000111000000000
00110000101000000000
00110000010000000000
00110000000000000000
->odca 01110110
01110110
01011110
00110010
00110000
->

J

life1d=: '_#'{~ (2 = 3+/\ 0,],0:)^:a:

{{out|Example use}}

   life1d ? 20 # 2
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________

Alternative implementation:

Rule=:2 :0 NB. , m: number of generations, n: rule number
  '_#'{~ (3 ((|.n#:~8#2) {~ #.)\ 0,],0:)^:(i.m)
)

{{out|Example use}}

   9 Rule 104 '#'='_###_##_#_#_#_#__#__'
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________

Java

This example requires a starting generation of at least length two (which is what you need for anything interesting anyway).

public class Life{
	public static void main(String[] args) throws Exception{
		String start= "_###_##_#_#_#_#__#__";
		int numGens = 10;
		for(int i= 0; i < numGens; i++){
			System.out.println("Generation " + i + ": " + start);
			start= life(start);
		}
	}

	public static String life(String lastGen){
		String newGen= "";
		for(int i= 0; i < lastGen.length(); i++){
			int neighbors= 0;
			if (i == 0){//left edge
				neighbors= lastGen.charAt(1) == '#' ? 1 : 0;
			} else if (i == lastGen.length() - 1){//right edge
				neighbors= lastGen.charAt(i - 1) == '#' ? 1 : 0;
			} else{//middle
				neighbors= getNeighbors(lastGen.substring(i - 1, i + 2));
			}

			if (neighbors == 0){//dies or stays dead with no neighbors
				newGen+= "_";
			}
			if (neighbors == 1){//stays with one neighbor
				newGen+= lastGen.charAt(i);
			}
			if (neighbors == 2){//flips with two neighbors
				newGen+= lastGen.charAt(i) == '#' ? "_" : "#";
			}
		}
		return newGen;
	}

	public static int getNeighbors(String group){
		int ans= 0;
		if (group.charAt(0) == '#') ans++;
		if (group.charAt(2) == '#') ans++;
		return ans;
	}
}

{{out}}

Generation 0: _###_##_#_#_#_#__#__
Generation 1: _#_#####_#_#_#______
Generation 2: __##___##_#_#_______
Generation 3: __##___###_#________
Generation 4: __##___#_##_________
Generation 5: __##____###_________
Generation 6: __##____#_#_________
Generation 7: __##_____#__________
Generation 8: __##________________
Generation 9: __##________________

{{trans|C}} In this version, b is replaced by a backup which is local to the evolve method, and the evolve method returns a boolean.

public class Life{
	private static char[] trans = "___#_##_".toCharArray();

	private static int v(StringBuilder cell, int i){
		return (cell.charAt(i) != '_') ? 1 : 0;
	}

	public static boolean evolve(StringBuilder cell){
		boolean diff = false;
		StringBuilder backup = new StringBuilder(cell.toString());

		for(int i = 1; i < cell.length() - 3; i++){
			/* use left, self, right as binary number bits for table index */
			backup.setCharAt(i, trans[v(cell, i - 1) * 4 + v(cell, i) * 2
			      					+ v(cell, i + 1)]);
			diff = diff || (backup.charAt(i) != cell.charAt(i));
		}

		cell.delete(0, cell.length());//clear the buffer
		cell.append(backup);//replace it with the new generation
		return diff;
	}

	public static void main(String[] args){
		StringBuilder  c = new StringBuilder("_###_##_#_#_#_#__#__\n");

		do{
			System.out.printf(c.substring(1));
		}while(evolve(c));
	}
}

{{out}}

###_##_#_#_#_#__#__
#_#####_#_#_#______
_##___##_#_#_______
_##___###_#________
_##___#_##_________
_##____###_________
_##____#_#_________
_##_____#__________
_##________________

JavaScript

The example below expects an array of 1s or 0s, as in the example. It also adds dead cells to both ends, which aren't included in the returned next generation.

state[i-1] refers to the new cell in question, (old[i] == 1) checks if the old cell was alive.

function caStep(old) {
  var old = [0].concat(old, [0]); // Surround with dead cells.
  var state = []; // The new state.

  for (var i=1; i<old.length-1; i++) {
    switch (old[i-1] + old[i+1]) {
      case 0: state[i-1] = 0; break;
      case 1: state[i-1] = (old[i] == 1) ? 1 : 0; break;
      case 2: state[i-1] = (old[i] == 1) ? 0 : 1; break;
    }
  }
  return state;
}

{{out|Example usage}}

alert(caStep([0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]));

shows an alert with "0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0".

jq

The main point of interest in the following is perhaps the way the built-in function "recurse" is used to continue the simulation until quiescence.

# The 1-d cellular automaton:
def next:
   # Conveniently, jq treats null as 0 when it comes to addition
   # so there is no need to fiddle with the boundaries
  . as $old
  | reduce range(0; length) as $i
    ([];
     ($old[$i-1] + $old[$i+1]) as $s
     | if   $s == 0 then .[$i] = 0
       elif $s == 1 then .[$i] = (if $old[$i] == 1 then 1 else 0 end)
       else              .[$i] = (if $old[$i] == 1 then 0 else 1 end)
       end);


# pretty-print an array:
def pp: reduce .[] as $i (""; . + (if $i == 0 then " " else "*" end));

# continue until quiescence:
def go: recurse(. as $prev | next | if . == $prev then empty else . end) | pp;

# Example:
[0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] | go

{{out}}

$ jq -c -r -n -f One-dimensional_cellular_automata.jq
 *** ** * * * *  *
 * ***** * * *
  **   ** * *
  **   *** *
  **   * **
  **    ***
  **    * *
  **     *
  **

Julia

This solution creates an automaton with with either empty or periodic bounds. The empty bounds case, is typical of many of the solutions here. The periodic bounds case is a typical physics approach where, in effect, the beginning and end of the list touch each other to form a circular rather than linear array. In practice, the effects of boundary conditions are subtle for long arrays.

function next_gen(a::BitArray{1}, isperiodic=false)
    b = copy(a)
    if isperiodic
        ncnt = prepend!(a[1:end-1], [a[end]]) + append!(a[2:end], [a[1]])
    else
        ncnt = prepend!(a[1:end-1], [false]) + append!(a[2:end], [false])
    end
    b[ncnt .== 0] = false
    b[ncnt .== 2] = ~b[ncnt .== 2]
    return b
end

function show_gen(a::BitArray{1})
    s = join([i ? "\u2588" : " " for i in a], "")
    s = "\u25ba"*s*"\u25c4"
end

hi = 70
a = bitrand(hi)
b = falses(hi)
println("A 1D Cellular Atomaton with ", hi, " cells and empty bounds.")
while any(a) && any(a .!= b)
    println("    ", show_gen(a))
    b = copy(a)
    a = next_gen(a)
end
a = bitrand(hi)
b = falses(hi)
println()
println("A 1D Cellular Atomaton with ", hi, " cells and periodic bounds.")
while any(a) && any(a .!= b)
    println("    ", show_gen(a))
    b = copy(a)
    a = next_gen(a, true)
end

{{out}}

A 1D Cellular Atomaton with 70 cells and empty bounds.
    ► ███  ██  █ ██   ███ █  ███  ██  █ █   ██████ █   ██ █ █ █  █ ██  ███ ◄
    ► █ █  ██   ███   █ ██   █ █  ██   █    █    ██    ███ █ █    ███  █ █ ◄
    ►  █   ██   █ █    ███    █   ██             ██    █ ██ █     █ █   █  ◄
    ►      ██    █     █ █        ██             ██     ████       █       ◄
    ►      ██           █         ██             ██     █  █               ◄
    ►      ██                     ██             ██                        ◄

A 1D Cellular Atomaton with 70 cells and periodic bounds.
    ►████   ██ █    █ █  ██  ██ █ █      ████   █    ███  ███ ██     ██ ██ ◄
    ►█  █   ███      █   ██  ███ █       █  █        █ █  █ ████     ██████◄
    ►█      █ █          ██  █ ██                     █    ██  █     █     ◄
    ►        █           ██   ███                          ██              ◄
    ►                    ██   █ █                          ██              ◄
    ►                    ██    █                           ██              ◄
    ►                    ██                                ██              ◄

K

f:{2=+/(0,x,0)@(!#x)+/:!3}

{{out|Example usage}}

   `0:"_X"@f\0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0
_XXX_XX_X_X_X_X__X__
_X_XXXXX_X_X_X______
__XX___XX_X_X_______
__XX___XXX_X________
__XX___X_XX_________
__XX____XXX_________
__XX____X_X_________
__XX_____X__________
__XX________________

Kotlin

{{trans|C}}

// version 1.1.4-3

val trans = "___#_##_"

fun v(cell: StringBuilder, i: Int) = if (cell[i] != '_') 1 else 0

fun evolve(cell: StringBuilder, backup: StringBuilder): Boolean {
    val len = cell.length - 2
    var diff = 0
    for (i in 1 until len) {
        /* use left, self, right as binary number bits for table index */
        backup[i] = trans[v(cell, i - 1) * 4 + v(cell, i) * 2 + v(cell, i + 1)]
        diff += if (backup[i] != cell[i]) 1 else 0
    }
    cell.setLength(0)
    cell.append(backup)
    return diff != 0
}

fun main(args: Array<String>) {
    val c = StringBuilder("_###_##_#_#_#_#__#__")
    val b = StringBuilder("____________________")
    do {
       println(c.substring(1))
    }
    while (evolve(c,b))
}

{{out}}

###_##_#_#_#_#__#__
#_#####_#_#_#______
_##___##_#_#_______
_##___###_#________
_##___#_##_________
_##____###_________
_##____#_#_________
_##_____#__________
_##________________

Liberty BASIC

'   [RC] 'One-dimensional cellular automata'

'    does not wrap so fails for some rules
rule$ ="00010110"   '   Rule 22 decimal

state$ ="0011101101010101001000"

for j =1 to 20
    print state$
    oldState$ =state$
    state$ ="0"
    for k =2 to len( oldState$) -1
        NHood$ =mid$( oldState$, k -1, 3)  '   pick 3 char neighbourhood and turn binary string to decimal
        vNHood =0
        for kk =3 to 1 step -1
            vNHood =vNHood +val( mid$( NHood$, kk, 1)) *2^( 3 -kk)
        next kk
                                        '  .... & use it to index into rule$ to find appropriate new value
        state$ =state$ +mid$( rule$, vNHood +1, 1)
    next k
    state$ =state$ +"0"

next j

end

Locomotive Basic

10 MODE 1:n=10:READ w:DIM x(w+1),x2(w+1):FOR i=1 to w:READ x(i):NEXT
20 FOR k=1 TO n
30 FOR j=1 TO w
40 IF x(j) THEN PRINT "#"; ELSE PRINT "_";
50 IF x(j-1)+x(j)+x(j+1)=2 THEN x2(j)=1 ELSE x2(j)=0
60 NEXT:PRINT
70 FOR j=1 TO w:x(j)=x2(j):NEXT
80 NEXT
90 DATA 20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0

{{out}} [[File:Cellular automaton locomotive basic.png]]

Logo

{{works with|UCB Logo}}

make "cell_list [0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0]
make "generations 9

to evolve :n
ifelse :n=1 [make "nminus1 item :cell_count :cell_list][make "nminus1 item :n-1 :cell_list]
ifelse :n=:cell_count[make "nplus1 item 1 :cell_list][make "nplus1 item :n+1 :cell_list]
ifelse ((item :n :cell_list)=0) [
	ifelse (and (:nminus1=1) (:nplus1=1)) [output 1][output (item :n :cell_list)]
][
	ifelse (and (:nminus1=1) (:nplus1=1)) [output 0][
	   ifelse and (:nminus1=0) (:nplus1=0) [output 0][output (item :n :cell_list)]]
]
end

to CA_1D :cell_list :generations
make "cell_count count :cell_list
(print ")
make "printout "
repeat :cell_count [
make "printout word :printout ifelse (item repcount :cell_list)=1 ["#]["_]
]
(print "Generation "0: :printout)

repeat :generations [
       (make "cell_list_temp [])
       repeat :cell_count[
             (make "cell_list_temp (lput (evolve repcount) :cell_list_temp))
       ]
       make "cell_list :cell_list_temp
       make "printout "
       repeat :cell_count [
       	      make "printout word :printout ifelse (item repcount :cell_list)=1 ["#]["_]
       ]
       (print "Generation  word repcount ": :printout)
]
end

CA_1D :cell_list :generations

{{out}}

Generation 0: _###_##_#_#_#_#__#__
Generation 1: _#_#####_#_#_#______
Generation 2: __##___##_#_#_______
Generation 3: __##___###_#________
Generation 4: __##___#_##_________
Generation 5: __##____###_________
Generation 6: __##____#_#_________
Generation 7: __##_____#__________
Generation 8: __##________________
Generation 9: __##________________

Lua

num_iterations = 9
f = { 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0 }

function Output( f, l )
    io.write( l, ":  " )
    for i = 1, #f do
        local c
        if f[i] == 1 then c = '#' else c = '_' end
        io.write( c )
    end
    print ""
end

Output( f, 0 )

for l = 1, num_iterations do
    local g = {}
    for i = 2, #f-1 do
        if f[i-1] + f[i+1] == 1 then
            g[i] = f[i]
        elseif f[i] == 0 and f[i-1] + f[i+1] == 2 then
            g[i] = 1
        else
            g[i] = 0
        end
    end
    if f[1]  == 1 and f[2]    == 1 then g[1]  = 1 else g[1]  = 0 end
    if f[#f] == 1 and f[#f-1] == 1 then g[#f] = 1 else g[#f] = 0 end
    f, g = g, f

    Output( f, l )
end

{{out}}

0:  _###_##_#_#_#_#__#__
1:  _#_#####_#_#_#______
2:  __##___##_#_#_______
3:  __##___###_#________
4:  __##___#_##_________
5:  __##____###_________
6:  __##____#_#_________
7:  __##_____#__________
8:  __##________________
9:  __##________________

M4

divert(-1)
define(`set',`define(`$1[$2]',`$3')')
define(`get',`defn(`$1[$2]')')
define(`setrange',`ifelse(`$3',`',$2,`define($1[$2],$3)`'setrange($1,
   incr($2),shift(shift(shift($@))))')')

dnl  throw in sentinels at each end (0 and size+1) to make counting easy
define(`new',`set($1,size,eval($#-1))`'setrange($1,1,
   shift($@))`'set($1,0,0)`'set($1,$#,0)')

define(`for',
   `ifelse($#,0,``$0'',
   `ifelse(eval($2<=$3),1,
   `pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
define(`show',
   `for(`k',1,get($1,size),`get($1,k) ')')

dnl  swap(`a',a,`b')  using arg stack for temp
define(`swap',`define(`$1',$3)`'define(`$3',$2)')
define(`nalive',
   `eval(get($1,decr($2))+get($1,incr($2)))')
setrange(`live',0,0,1,0)
setrange(`dead',0,0,0,1)
define(`nv',
   `ifelse(get($1,z),0,`get(dead,$3)',`get(live,$3)')')
define(`evolve',
   `for(`z',1,get($1,size),
      `set($2,z,nv($1,z,nalive($1,z)))')')
new(`a',0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0)
set(`b',size,get(`a',size))`'set(`b',0,0)`'set(`b',incr(get(`a',size)),0)
define(`x',`a')
define(`y',`b')
divert
for(`j',1,10,
   `show(x)`'evolve(`x',`y')`'swap(`x',x,`y')
')`'show(x)

{{out}}

0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0
0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0
0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0
0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

=={{header|Mathematica}} / {{header|Wolfram Language}}== Built-in function:

CellularAutomaton[{{0,0,_}->0,{0,1,0}->0,{0,1,1}->1,{1,0,0}->0,{1,0,1}->1,{1,1,0}->1,{1,1,1}->0},{{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1},0},12]
Print @@@ (% /. {1 -> "#", 0 -> "."});

For succinctness, an integral rule can be used:

CellularAutomaton[2^^01101000 (* == 104 *), {{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1}, 0}, 12];

{{out}}

###.##.#.#.#.#..#
#.#####.#.#.#....
.##...##.#.#.....
.##...###.#......
.##...#.##.......
.##....###.......
.##....#.#.......
.##.....#........
.##..............
.##..............
.##..............
.##..............
.##..............

=={{header|MATLAB}} / {{header|Octave}}==

function one_dim_cell_automata(v,n)
   V='_#';
   while n>=0;
	disp(V(v+1));
	n = n-1;
	v = filter([1,1,1],1,[0,v,0]);
	v = v(3:end)==2;
   end;
end

{{out}}

octave:27> one_dim_cell_automata('01110110101010100100'=='1',20);
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________
...

=={{header|Modula-3}}== {{trans|Ada}}

Modula-3 provides a module Word for doing bitwise operations, but it segfaults when trying to use BOOLEAN types, so we use INTEGER instead.

MODULE Cell EXPORTS Main;

IMPORT IO, Fmt, Word;

VAR culture := ARRAY [0..19] OF INTEGER {0, 1, 1, 1,
                                         0, 1, 1, 0,
                                         1, 0, 1, 0,
                                         1, 0, 1, 0,
                                         0, 1, 0, 0};

PROCEDURE Step(VAR culture: ARRAY OF INTEGER) =
  VAR left: INTEGER := 0;
      this, right: INTEGER;
  BEGIN
    FOR i := FIRST(culture) TO LAST(culture) - 1 DO
      right := culture[i + 1];
      this := culture[i];
      culture[i] :=
          Word.Or(Word.And(this, Word.Xor(left, right)), Word.And(Word.Not(this), Word.And(left, right)));
      left := this;
    END;
    culture[LAST(culture)] := Word.And(culture[LAST(culture)], Word.Not(left));
  END Step;

PROCEDURE Put(VAR culture: ARRAY OF INTEGER) =
  BEGIN
    FOR i := FIRST(culture) TO LAST(culture) DO
      IF culture[i] = 1 THEN
        IO.PutChar('#');
      ELSE
        IO.PutChar('_');
      END;
    END;
  END Put;

BEGIN
  FOR i := 0 TO 9 DO
    IO.Put("Generation " & Fmt.Int(i) & " ");
    Put(culture);
    IO.Put("\n");
    Step(culture);
  END;
END Cell.

{{out}}

Generation 0 _###_##_#_#_#_#__#__
Generation 1 _#_#####_#_#_#______
Generation 2 __##___##_#_#_______
Generation 3 __##___###_#________
Generation 4 __##___#_##_________
Generation 5 __##____###_________
Generation 6 __##____#_#_________
Generation 7 __##_____#__________
Generation 8 __##________________
Generation 9 __##________________

MontiLang

30 VAR length .
35 VAR height .
FOR length 0 ENDFOR 1 0 ARR VAR list .
length 1 - VAR topLen .
FOR topLen 0 ENDFOR 1 ARR VAR topLst .

DEF getNeighbors
    1 - VAR tempIndex .
    GET tempIndex SWAP
    tempIndex 1 + VAR tempIndex .
    GET tempIndex SWAP
    tempIndex 1 + VAR tempIndex .
    GET tempIndex SWAP .
    FOR 3 TOSTR ROT ENDFOR
    FOR 2 SWAP + ENDFOR
ENDDEF

DEF printArr
    LEN 1 - VAR stLen .
    0 VAR j .
    FOR stLen
        GET j
        TOSTR OUT .
        j 1 + VAR j .
    ENDFOR
    || PRINT .
ENDDEF

FOR height
    FOR length 0 ENDFOR ARR VAR next .
    1 VAR i .
    FOR length
        list i getNeighbors VAR last .
        i 1 - VAR ind .
        last |111| ==
        IF : .
            next 0 INSERT ind
        ENDIF

        last |110| ==
        IF : .
            next 1 INSERT ind
        ENDIF

        last |101| ==
        IF : .
            next 1 INSERT ind
        ENDIF

        last |100| ==
        IF : .
            next 0 INSERT ind
        ENDIF

        last |011| ==
        IF : .
            next 1 INSERT ind
        ENDIF

        last |010| ==
        IF : .
            next 1 INSERT ind
        ENDIF

        last |001| ==
        IF : .
            next 1 INSERT ind
        ENDIF

        last |000| ==
        IF : .
            next 0 INSERT ind
        ENDIF
        clear
        i 1 + VAR i .
    ENDFOR
    next printArr .
    next 0 ADD APPEND . VAR list .
ENDFOR

Nial

(life.nial)

% we need a way to write a values and pass the same back
wi is rest link [write, pass]
% calculate the neighbors by rotating the array left and right and joining them
neighbors is pack [pass, sum [-1 rotate,  1 rotate]]
% calculate the individual birth and death of a single array element
igen is fork [ = [ + [first, second], 3 first], 0 first, = [ + [first, second], 2 first], 1 first, 0 first ]
% apply that to the array
nextgen is each igen neighbors
% 42
life is fork [ > [sum pass, 0 first], life nextgen wi, pass ]

{{out|Using it}}

|loaddefs 'life.nial'
|I := [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
|life I

Nim

import random


type
  BoolArray  = array[30, bool]
  Symbols    = array[bool, char]


proc neighbours(map: BoolArray, i: int): int =
  if i > 0:             inc(result, int(map[i - 1]))
  if i + 1 < len(map):  inc(result, int(map[i + 1]))

proc print(map: BoolArray, symbols: Symbols) =
  for i in map: write(stdout, symbols[i])
  write(stdout, "\l")

proc randomMap: BoolArray =
  randomize()
  for i in mitems(result): i = rand([true, false])


const
  num_turns = 20
  symbols   = ['_', '#']

  T = true
  F = false

var map =
  [F, T, T, T, F, T, T, F, T, F, T, F, T, F, T,
    F, F, T, F, F, F, F, F, F, F, F, F, F, F, F]

# map = randomMap()  # uncomment for random start

print(map, symbols)

for _ in 0 ..< num_turns:
  var map2 = map

  for i, v in pairs(map):
    map2[i] =
      if v: neighbours(map, i) == 1
      else: neighbours(map, i) == 2

  print(map2, symbols)

  if map2 == map: break
  map = map2

{{out}}

_###_##_#_#_#_#__#____________
_#_#####_#_#_#________________
__##___##_#_#_________________
__##___###_#__________________
__##___#_##___________________
__##____###___________________
__##____#_#___________________
__##_____#____________________
__##__________________________
__##__________________________

'''Using a string character counting method''':

const
  s_init: string = "_###_##_#_#_#_#__#__"
  arrLen: int = 20

var q0: string = s_init & repeatChar(arrLen-20,'_')
var q1: string = q0

proc life(s:string): char =
   var str: string = s
   if len(normalize(str)) == 2:      # normalize eliminates underscores
      return '#'
   return '_'

proc evolve(q: string): string =
   result = repeatChar(arrLen,'_')
   #result[0] = '_'
   for i in 1 .. q.len-1:
      result[i] = life(substr(q & '_',i-1,i+1))

echo(q1)
q1 = evolve(q0)
echo(q1)
while q1 != q0:
   q0 = q1
   q1 = evolve(q0)
   echo(q1)

{{out}}

_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________

'''Using nested functions and method calling style:'''

proc cell_automata =
    proc evolve_into(X, T : var string) =
        for i in X.low..X.high:
            let
                alive = X[i] == 'o'
                left  = if i == X.low:  false else: X[i - 1] == 'o'
                right = if i == X.high: false else: X[i + 1] == 'o'
            T[i] =
                if alive: if left xor right: 'o' else: '.'
                else:     if left and right: 'o' else: '.'

    var
        X = ".ooo.oo.o.o.o.o..o.."
        T = X

    for i in 1..10:
        X.echo
        X.evolve_into T
        T.swap X

OCaml

let get g i =
  try g.(i)
  with _ -> 0

let next_cell g i =
  match get g (i-1), get g (i), get g (i+1) with
  | 0, 0, 0 -> 0
  | 0, 0, 1 -> 0
  | 0, 1, 0 -> 0
  | 0, 1, 1 -> 1
  | 1, 0, 0 -> 0
  | 1, 0, 1 -> 1
  | 1, 1, 0 -> 1
  | 1, 1, 1 -> 0
  | _ -> assert(false)

let next g =
  let old_g = Array.copy g in
  for i = 0 to pred(Array.length g) do
    g.(i) <- (next_cell old_g i)
  done

let print_g g =
  for i = 0 to pred(Array.length g) do
    if g.(i) = 0
    then print_char '_'
    else print_char '#'
  done;
  print_newline()

put the code above in a file named "life.ml", and then use it in the ocaml toplevel like this:

#use "life.ml" ;;

let iter n g =
  for i = 0 to n do
    Printf.printf "Generation %d: " i; print_g g;
    next g;
  done
;;

let g_of_string str =
  let f = (function '_' -> 0 | '#' -> 1 | _ -> assert false) in
  Array.init (String.length str) (fun i -> f str.[i])
;;

# iter 9 (g_of_string "_###_##_#_#_#_#__#__") ;;
Generation 0: _###_##_#_#_#_#__#__
Generation 1: _#_#####_#_#_#______
Generation 2: __##___##_#_#_______
Generation 3: __##___###_#________
Generation 4: __##___#_##_________
Generation 5: __##____###_________
Generation 6: __##____#_#_________
Generation 7: __##_____#__________
Generation 8: __##________________
Generation 9: __##________________
- : unit = ()

```



## Oforth



```Oforth
: nextGen( l )
| i s |
   l byteSize dup ->s String newSize
   s loop: i [
      i 1 if=: [ 0 ] else: [ i 1- l byteAt '#' = ]
      i l byteAt '#' = +
      i s if=: [ 0 ] else: [ i 1+ l byteAt '#' = ] +
      2 if=: [ '#' ] else: [ '_' ] over add
      ]
;

: gen( l n -- )
    l dup .cr #[ nextGen dup .cr ] times( n ) drop ;
```


{{out}}

```txt

"_###_##_#_#_#_#__#__" 10 gen
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________
ok

```



## Oz


```oz
declare
  A0 = {List.toTuple unit "_###_##_#_#_#_#__#__"}

  MaxGenerations = 9

  Rules = unit('___':&_
               '__#':&_
               '_#_':&_
               '_##':&#
               '#__':&_
               '#_#':&#
               '##_':&#
               '###':&_)

  fun {Evolve A}
     {Record.mapInd A
      fun {$ I V}
         Left = {CondSelect A I-1 &_}
         Right = {CondSelect A I+1 &_}
         Env = {String.toAtom [Left V Right]}
      in
         Rules.Env
      end
     }
  end

  fun lazy {Iterate X F}
     X|{Iterate {F X} F}
  end
in
  for
     I in 0..MaxGenerations
     A in {Iterate A0 Evolve}
  do
     {System.showInfo "Gen. "#I#": "#{Record.toList A}}
  end
```


{{out}}

```txt
Gen. 0: _###_##_#_#_#_#__#__
Gen. 1: _#_#####_#_#_#______
Gen. 2: __##___##_#_#_______
Gen. 3: __##___###_#________
Gen. 4: __##___#_##_________
Gen. 5: __##____###_________
Gen. 6: __##____#_#_________
Gen. 7: __##_____#__________
Gen. 8: __##________________
Gen. 9: __##________________

```



## PARI/GP

This version defines the fixed cells to the left and right as dead;
of course other versions are possible.
This function generates one generation from a previous one,
passed as a 0-1 vector.

```parigp
step(v)=my(u=vector(#v),k);u[1]=v[1]&v[2];u[#u]=v[#v]&v[#v-1];for(i=2,#v-1,k=v[i-1]+v[i+1];u[i]=if(v[i],k==1,k==2));u;
```


To simulate a run of 10 generations of the automaton, the function above can be put in a loop that spawns a new generation as a function of nth generations passed (n=0 is the initial state):


```parigp
cur = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]; for(n=0, 9, print(cur); cur = step(cur));
```



###  Output


[0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]
[0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

```



## Pascal


```pascal
program Test;
{$IFDEF FPC}{$MODE DELPHI}{$ELSE}{$APPTYPE}{$ENDIF}
uses
  sysutils;
const
  cCHAR: array[0..1] of char = ('_','#');
type
  TRow =  array of byte;

function ConvertToRow(const s:string):tRow;
var
  i : NativeInt;
Begin
  i := length(s);
  setlength(Result,length(s));
  For i := i downto 0 do
    result[i-1]:= ORD(s[i]=cChar[1]);
end;

function OutRow(const row:tRow):string;
//create output string
var
  i: NativeInt;
Begin
  i := length(row);
  setlength(result,i);
  For i := i downto 1 do
    result[i]:= cChar[row[i-1]];
end;

procedure NextRow(row:pByteArray;MaxIdx:NativeInt);
//compute next row in place by the using a small storage for the
//2 values, that would otherwise be overridden
var
  leftValue,Value: NativeInt;
  i,trpCnt: NativeInt;
Begin
  leftValue := 0;
  trpCnt := row[0]+row[1];

  i := 0;
  while i < MaxIdx do
  Begin
    Value := row[i];
    //the rule for survive : PopCnt == 2
    row[i] := ORD(trpCnt= 2);
    //reduce popcnt of element before
    dec(trpCnt,leftValue);
    //goto next element
    inc(i);
    leftValue := Value;
    //increment popcnt by right element
    inc(trpCnt,row[i+1]);
    //move to next position in ring buffer
  end;
  row[MaxIdx] := ORD(trpCnt= 2);
end;

const
  TestString: string='  ### ## # # # #  #  ';
var
  s: string;
  row:tRow;
  i: NativeInt;
begin
  s := Teststring;
  row:= ConvertToRow(s);
  For i := 0 to 9 do
  Begin
    writeln(OutRow(row));
    NextRow(@row[0],High(row));
  end;
end.
```

{{Out}}
```txt

__###_##_#_#_#_#__#__
__#_#####_#_#_#______
___##___##_#_#_______
___##___###_#________
___##___#_##_________
___##____###_________
___##____#_#_________
___##_____#__________
___##________________
___##________________
```



## Perl


Use regexp to extract and substitute cells while the string changes

Convert cells to zeros and ones to set complement state

```perl

$_="_###_##_#_#_#_#__#__\n";
do {
  y/01/_#/;
  print;
  y/_#/01/;
  s/(?<=(.))(.)(?=(.))/$1 == $3 ? $1 ? 1-$2 : 0 : $2/eg;
} while ($x ne $_ and $x=$_);

```


Use hash for complement state

```perl

$_="_###_##_#_#_#_#__#__\n";
%h=qw(# _ _ #);
do {
  print;
  s/(?<=(.))(.)(?=(.))/$1 eq $3 ? $1 eq "_" ? "_" : $h{$2} : $2/eg;
} while ($x ne $_ and $x=$_);

```


{{out}} for both versions:

```txt
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
```



## Perl 6

{{works with|rakudo|2014-02-27}}
We'll make a general algorithm capable of computing any cellular automata
as defined by [[wp:Stephen Wolfram|Stephen Wolfram]]'s
famous book ''[[wp:A new kind of Science|A new kind of Science]]''.
We will take the liberty of wrapping the array of cells
as it does not affect the result much
and it makes the implementation a lot easier.


```perl6
class Automaton {
    has $.rule;
    has @.cells;
    has @.code = $!rule.fmt('%08b').flip.comb».Int;

    method gist { "|{ @!cells.map({+$_ ?? '#' !! ' '}).join }|" }

    method succ {
        self.new: :$!rule, :@!code, :cells(
            @!code[
                    4 «*« @!cells.rotate(-1)
                »+« 2 «*« @!cells
                »+«       @!cells.rotate(1)
            ]
        )
    }
}

#  The rule proposed for this task is rule 0b01101000 = 104

my @padding = 0 xx 5;
my Automaton $a .= new:
    rule  => 104,
    cells => flat @padding, '111011010101'.comb, @padding
;
say $a++ for ^10;


# Rule 104 is not particularly interesting so here is [[wp:Rule 90|Rule 90]],
# which shows a [[wp:Sierpinski Triangle|Sierpinski Triangle]].

say '';
@padding = 0 xx 25;
$a = Automaton.new: :rule(90), :cells(flat @padding, 1, @padding);

say $a++ for ^20;
```


{{out}}

```txt

|     ### ## # # #     |
|     # ##### # #      |
|      ##   ## #       |
|      ##   ###        |
|      ##   # #        |
|      ##    #         |
|      ##              |
|      ##              |
|      ##              |
|      ##              |

|                         #                         |
|                        # #                        |
|                       #   #                       |
|                      # # # #                      |
|                     #       #                     |
|                    # #     # #                    |
|                   #   #   #   #                   |
|                  # # # # # # # #                  |
|                 #               #                 |
|                # #             # #                |
|               #   #           #   #               |
|              # # # #         # # # #              |
|             #       #       #       #             |
|            # #     # #     # #     # #            |
|           #   #   #   #   #   #   #   #           |
|          # # # # # # # # # # # # # # # #          |
|         #                               #         |
|        # #                             # #        |
|       #   #                           #   #       |
|      # # # #                         # # # #      |

```



## Phix

Ludicrously optimised:

```Phix
string s = "_###_##_#_#_#_#__#__"
integer prev='_', curr, toggled = 1

while 1 do
    ?s
    for i=2 to length(s)-1 do
        curr = s[i]
        if prev=s[i+1]
        and (curr='#' or prev='#') then
            s[i] = 130-curr
            toggled = 1
        end if
        prev = curr
    end for
    if not toggled then ?s exit end if
    toggled = 0
end while
```

{{out}}
"_###_##_#_#_#_#__#__"
"_#_#####_#_#_#______"
"__##___##_#_#_______"
"__##___###_#________"
"__##___#_##_________"
"__##____###_________"
"__##____#_#_________"
"__##_____#__________"
"__##________________"
"__##________________"

```

And of course I had to have a crack at that Sierpinski_Triangle:

```Phix
string s = "________________________#________________________"
integer prev='_', curr, toggled = 1

for limit=1 to 24 do
    ?s
    for i=2 to length(s)-1 do
        curr = s[i]
        if (prev=s[i+1]) = (curr='#') then
            s[i] = 130-curr
        end if
        prev = curr
    end for
end for
```

{{out}}
"________________________#________________________"
"_______________________#_#_______________________"
"______________________#___#______________________"
"_____________________#_#_#_#_____________________"
"____________________#_______#____________________"
"___________________#_#_____#_#___________________"
"__________________#___#___#___#__________________"
"_________________#_#_#_#_#_#_#_#_________________"
"________________#_______________#________________"
"_______________#_#_____________#_#_______________"
"______________#___#___________#___#______________"
"_____________#_#_#_#_________#_#_#_#_____________"
"____________#_______#_______#_______#____________"
"___________#_#_____#_#_____#_#_____#_#___________"
"__________#___#___#___#___#___#___#___#__________"
"_________#_#_#_#_#_#_#_#_#_#_#_#_#_#_#_#_________"
"________#_______________________________#________"
"_______#_#_____________________________#_#_______"
"______#___#___________________________#___#______"
"_____#_#_#_#_________________________#_#_#_#_____"
"____#_______#_______________________#_______#____"
"___#_#_____#_#_____________________#_#_____#_#___"
"__#___#___#___#___________________#___#___#___#__"
"_#_#_#_#_#_#_#_#_________________#_#_#_#_#_#_#_#_"

```



## PicoLisp


```PicoLisp
(let Cells (chop "_###_##_#_#_#_#__#__")
   (do 10
      (prinl Cells)
      (setq Cells
         (make
            (link "_")
            (map
               '((L)
                  (case (head 3 L)
                     (`(mapcar chop '("___" "__#" "_#_" "#__" "###"))
                         (link "_") )
                     (`(mapcar chop '("_##" "#_#" "##_"))
                        (link "#") ) ) )
               Cells )
            (link "_") ) ) ) )
```

{{out}}

```txt
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
```



## Prolog

Works ith SWI-Prolog.

```Prolog
one_dimensional_cellular_automata(L) :-
	maplist(my_write, L), nl,
	length(L, N),
	length(LN, N),
	% there is a 0 before the beginning
	compute_next([0 |L], LN),
	(   L \= LN -> one_dimensional_cellular_automata(LN); true).

% All the possibilites
compute_next([0, 0, 0 | R], [0 | R1]) :-
	compute_next([0, 0 | R], R1).

compute_next([0, 0, 1 | R], [0 | R1]) :-
	compute_next([0, 1 | R], R1).

compute_next([0, 1, 0 | R], [0 | R1]) :-
	compute_next([1, 0 | R], R1).

compute_next([0, 1, 1 | R], [1 | R1]) :-
	compute_next([1, 1 | R], R1).

compute_next([1, 0, 0 | R], [0 | R1]) :-
	compute_next([0, 0 | R], R1).

compute_next([1, 0, 1 | R], [1 | R1]) :-
	compute_next([0, 1 | R], R1).

compute_next([1, 1, 0 | R], [1 | R1]) :-
	compute_next([1, 0 | R], R1).

compute_next([1, 1, 1 | R], [0 | R1]) :-
	compute_next([1, 1 | R], R1).

% the last four possibilies =>
% we consider that there is à 0  after the end
complang jq># The 1-d cellular automaton:
def next:
   # Conveniently, jq treats null as 0 when it comes to addition
   # so there is no need to fiddle with the boundaries
  . as $old
  | reduce range(0; length) as $i
    ([];
     ($old[$i-1] + $old[$i+1]) as $s
     | if   $s == 0 then .[$i] = 0
       elif $s == 1 then .[$i] = (if $old[$i] == 1 then 1 else 0 end)
       else              .[$i] = (if $old[$i] == 1 then 0 else 1 end)
       end);


# pretty-print an array:
def pp: reduce .[] as $i (""; . + (if $i == 0 then " " else "*" end));

# continue until quiescence:
def go: recurse(. as $prev | next | if . == $prev then empty else . end) | pp;

# Example:
[0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] | goute_next([0, 0], [0]).

compute_next([1, 0], [0]).

compute_next([0, 1], [0]).

compute_next([1, 1], [1]).

my_write(0) :-
	write(.).

my_write(1) :-
	write(#).

one_dimensional_cellular_automata :-
	L = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0],
	one_dimensional_cellular_automata(L).

```

{{out}}

```txt
 ?- one_dimensional_cellular_automata.
.###.##.#.#.#.#..#..
.#.#####.#.#.#......
..##...##.#.#.......
..##...###.#........
..##...#.##.........
..##....###.........
..##....#.#.........
..##.....#..........
..##................
true .

```



## PureBasic


```PureBasic
EnableExplicit
Dim cG.i(21)
Dim nG.i(21)
Define.i n, Gen

DataSection
  Data.i 0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0
EndDataSection
For n=1 To 20
  Read.i cG(n)
Next

OpenConsole()
Repeat
  Print("Generation "+Str(Gen)+": ")
  For n=1 To 20
    Print(Chr(95-cG(n)*60))
  Next
  Gen +1
  PrintN("")
  For n=1 To 20
    If (cG(n) And (cG(n-1) XOr cg(n+1))) Or (Not cG(n) And (cG(n-1) And cg(n+1)))
     nG(n)=1
   Else
     nG(n)=0
   EndIf
  Next
  CopyArray(nG(), cG())
Until Gen > 9

PrintN("Press any key to exit"): Repeat: Until Inkey() <> ""
```

{{out}}

```txt
Generation 0: _###_##_#_#_#_#__#__
Generation 1: _#_#####_#_#_#______
Generation 2: __##___##_#_#_______
Generation 3: __##___###_#________
Generation 4: __##___#_##_________
Generation 5: __##____###_________
Generation 6: __##____#_#_________
Generation 7: __##_____#__________
Generation 8: __##________________
Generation 9: __##________________
```



## Python


### Procedural


### =Python: Straightforward interpretation of spec=


```python
import random

printdead, printlive = '_#'
maxgenerations = 10
cellcount = 20
offendvalue = '0'

universe = ''.join(random.choice('01') for i in range(cellcount))

neighbours2newstate = {
 '000': '0',
 '001': '0',
 '010': '0',
 '011': '1',
 '100': '0',
 '101': '1',
 '110': '1',
 '111': '0',
 }

for i in range(maxgenerations):
    print "Generation %3i:  %s" % ( i,
          universe.replace('0', printdead).replace('1', printlive) )
    universe = offendvalue + universe + offendvalue
    universe = ''.join(neighbours2newstate[universe[i:i+3]] for i in range(cellcount))
```

{{out}}

```txt
Generation   0:  _###_##_#_#_#_#__#__
Generation   1:  _#_#####_#_#_#______
Generation   2:  __##___##_#_#_______
Generation   3:  __##___###_#________
Generation   4:  __##___#_##_________
Generation   5:  __##____###_________
Generation   6:  __##____#_#_________
Generation   7:  __##_____#__________
Generation   8:  __##________________
Generation   9:  __##________________
```



### =Python: Using boolean operators on bits=

The following implementation uses boolean operations to realize the function.

```python
import random

nquads = 5
maxgenerations = 10
fmt = '%%0%ix'%nquads
nbits = 4*nquads
a = random.getrandbits(nbits)  << 1
#a = int('01110110101010100100', 2) << 1
endmask = (2<>1)))))
   a |= endvals
   a = ((a&((a<<1) | (a>>1))) ^ ((a<<1)&(a>>1))) & endmask
```



### =Python: Sum neighbours == 2=

This example makes use of the observation that a cell is alive in the next generation if the sum with its current neighbours of alive cells is two.

```python>>>
 gen = [ch == '#' for ch in '_###_##_#_#_#_#__#__']
>>> for n in range(10):
	print(''.join('#' if cell else '_' for cell in gen))
	gen = [0] + gen + [0]
	gen = [sum(gen[m:m+3]) == 2 for m in range(len(gen)-2)]


_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
>>>
```



### Composition of pure functions


Interpreting the rule shown in the task description as Wolfram rule 104, and generalising enough to allow for other rules of this kind:

```python
"""Cellular Automata"""

from itertools import (islice, repeat)
from random import randint


# ruleSample :: Int -> String
def ruleSample(intRule):
    '''16 steps in the evolution of a specified Wolfram rule.'''
    return 'Rule ' + str(intRule) + ':\n' + (
        unlines(map(
            showCells,
            take(16)(
                iterate(nextRowByRule(intRule))(
                    onePixelInLineOf(64) if bool(randint(0, 1)) else (
                        randomPixelsInLineOf(64)
                    )
                )
            )
        ))
    )


# nextRowByRule :: Int -> [Bool] -> [Bool]
def nextRowByRule(intRule):
    '''A row of booleans derived by Wolfram rule n
       from another boolean row of the same length.'''

    # step :: (Bool, Bool, Bool) -> Bool
    def step(l, x, r):
        return bool(intRule & 2**intFromBools([l, x, r]))

    # go :: [Bool] -> Bool
    def go(xs):
        return [False] + list(map(
            step,
            xs, xs[1:], xs[2:]
        )) + [False]
    return lambda xs: go(xs)


# TEST ----------------------------------------------------
# main :: IO ()
def main():
    '''Samples of Wolfram rule evolutions.'''

    print(
        unlines(map(ruleSample, [104, 30, 110]))
    )


# boolsFromInt :: Int -> [Bool]
def boolsFromInt(n):
    '''List of booleans derived by binary
       decomposition of an integer.'''
    def go(x):
        return Just((x // 2, bool(x % 2))) if x else Nothing()
    return unfoldl(go)(n)


# intFromBools :: [Bool] -> Int
def intFromBools(xs):
    '''Integer derived by binary interpretation
       of a list of booleans.'''
    def go(b, pn):
        power, n = pn
        return (2 * power, n + power if b else n)
    return foldr(go)([1, 0])(xs)[1]


# nBoolsFromInt :: Int -> Int -> [Bool]
def nBoolsFromInt(n):
    '''List of bools, left-padded to given length n,
       derived by binary decomposition of an integer x.'''
    def go(n, x):
        bs = boolsFromInt(x)
        return list(repeat(False, n - len(bs))) + bs
    return lambda x: go(n, x)


# onePixelInLineOf :: Int -> [Bool]
def onePixelInLineOf(n):
    '''A row of n (mainly False) booleans,
       with a single True value in the middle.'''
    return nBoolsFromInt(n)(
        2**(n // 2)
    )


# randomPixelsInLineOf :: Int -> [Bool]
def randomPixelsInLineOf(n):
    '''A row of n booleans with pseudorandom values.'''
    return [bool(randint(0, 1)) for _ in range(1, 1 + n)]


# showCells :: [Bool] -> String
def showCells(xs):
    '''A block string representation of a list of booleans.'''
    return ''.join([chr(9608) if x else ' ' for x in xs])


# GENERIC -------------------------------------------------

# Just :: a -> Maybe a
def Just(x):
    '''Constructor for an inhabited Maybe (option type) value.'''
    return {'type': 'Maybe', 'Nothing': False, 'Just': x}


# Nothing :: Maybe a
def Nothing():
    '''Constructor for an empty Maybe (option type) value.'''
    return {'type': 'Maybe', 'Nothing': True}


# foldr :: (a -> b -> b) -> b -> [a] -> b
def foldr(f):
    '''Right to left reduction of a list,
       using a binary operator.'''
    def go(v, xs):
        a = v
        for x in xs:
            a = f(x, a)
        return a
    return lambda acc: lambda xs: go(acc, xs[::-1])


# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
    '''An infinite list of repeated applications of f to x.'''
    def go(x):
        v = x
        while True:
            yield v
            v = f(v)
    return lambda x: go(x)


# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
    '''The prefix of xs of length n,
       or xs itself if n > length xs.'''
    return lambda xs: (
        xs[0:n]
        if isinstance(xs, list)
        else list(islice(xs, n))
    )


# unfoldl(lambda x: Just(((x - 1), x)) if 0 != x else Nothing())(10)
# -> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
# unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
    '''Dual to reduce or foldl.
       Where these reduce a list to a summary value, unfoldl
       builds a list from a seed value.
       Where f returns Just(a, b), a is appended to the list,
       and the residual b is used as the argument for the next
       application of f.
       When f returns Nothing, the completed list is returned.'''
    def go(v):
        xr = v, v
        xs = []
        while True:
            mb = f(xr[0])
            if mb.get('Nothing'):
                return xs
            else:
                xr = mb.get('Just')
                xs.insert(0, xr[1])
        return xs
    return lambda x: go(x)


# unlines :: [String] -> String
def unlines(xs):
    '''A single newline-delimited string derived
       from a list of strings.'''
    return '\n'.join(xs)


# MAIN -------------------------------------------------
if __name__ == '__main__':
    main()
```

{{Out}}

```txt
Rule 104:
    █  █  ████  ██    █   █      █ █ █ ██    █████ ██  ██  █ ██
          █  █  ██                █ █ ███    █   ████  ██   ███
                ██                 █ ██ █        █  █  ██   █ █
                ██                  ████               ██    █
                ██                  █  █               ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
                ██                                     ██
Rule 30:
                               █
                              ███
                             ██  █
                            ██ ████
                           ██  █   █
                          ██ ████ ███
                         ██  █    █  █
                        ██ ████  ██████
                       ██  █   ███     █
                      ██ ████ ██  █   ███
                     ██  █    █ ████ ██  █
                    ██ ████  ██ █    █ ████
                   ██  █   ███  ██  ██ █   █
                  ██ ████ ██  ███ ███  ██ ███
                 ██  █    █ ███   █  ███  █  █
                ██ ████  ██ █  █ █████  ███████
Rule 110:
█  █  ██ ██  ██  █ █  ██  ███ █ █ ███     ██ ██    █    █   █
  ██ ██████ ███ ████ ███ ██ ███████ █    ██████   ██   ██  ██
 █████    ███ ███  ███ ██████     ███   ██    █  ███  ███ ███
 █   █   ██ ███ █ ██ ███    █    ██ █  ███   ██ ██ █ ██ ███ █
 █  ██  █████ ████████ █   ██   █████ ██ █  █████████████ ███
 █ ███ ██   ███      ███  ███  ██   ██████ ██           ███ █
 ███ ████  ██ █     ██ █ ██ █ ███  ██    ████          ██ ███
 █ ███  █ █████    ████████████ █ ███   ██  █         █████ █
 ███ █ ████   █   ██          █████ █  ███ ██        ██   ███
 █ █████  █  ██  ███         ██   ███ ██ ████       ███  ██ █
 ███   █ ██ ███ ██ █        ███  ██ ██████  █      ██ █ █████
 █ █  ███████ ██████       ██ █ █████    █ ██     ███████   █
 ███ ██     ███    █      ███████   █   █████    ██     █  ██
 █ ████    ██ █   ██     ██     █  ██  ██   █   ███    ██ ███
 ███  █   █████  ███    ███    ██ ███ ███  ██  ██ █   █████ █
 █ █ ██  ██   █ ██ █   ██ █   █████ ███ █ ███ █████  ██   ███
```



## R



```R
set.seed(15797, kind="Mersenne-Twister")

maxgenerations = 10
cellcount = 20
offendvalue = FALSE

## Cells are alive if TRUE, dead if FALSE
universe <- c(offendvalue,
              sample( c(TRUE, FALSE), cellcount, replace=TRUE),
              offendvalue)

## List of patterns in which the cell stays alive
stayingAlive <- lapply(list(c(1,1,0),
                            c(1,0,1),
                            c(0,1,0)), as.logical)

## x : length 3 logical vector
## map: list of length 3 logical vectors that map to patterns
##      in which x stays alive
deadOrAlive <- function(x, map) list(x) %in% map

cellularAutomata <- function(x, map) {
    c(x[1], apply(embed(x, 3), 1, deadOrAlive, map=map), x[length(x)])
}

deadOrAlive2string <- function(x) {
    paste(ifelse(x, '#', '_'), collapse="")
}

for (i in 1:maxgenerations) {
    universe <- cellularAutomata(universe, stayingAlive)
    cat(format(i, width=3), deadOrAlive2string(universe), "\n")
}
```


{{out}}

```txt

  1 _##_____####_#___#_#__
  2 _##_____#__##_____#___
  3 _##________##_________
  4 _##________##_________
  5 _##________##_________
  6 _##________##_________
  7 _##________##_________
  8 _##________##_________
  9 _##________##_________
 10 _##________##_________

```



## Racket


```racket
#lang racket

(define (update cells)
  (for/list ([crowding (map +
                            (append '(0) (drop-right cells 1))
                            cells
                            (append (drop cells 1) '(0)))])
    (if (= 2 crowding) 1 0)))

(define (life-of cells time)
  (unless (zero? time)
    (displayln cells)
    (life-of (update cells) (sub1 time))))

(life-of '(0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0)
         10)

#| (0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0)
   (0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
   (0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0) |#
```


Below is an alternative implementation using graphical output in the Racket REPL.
It works with DrRacket and Emacs + Geiser.

```racket
#lang slideshow

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Simulation of cellular automata, as described by Stephen Wolfram in his 1983 paper.
;; Uses Racket's inline image display capability for visual presentation
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(require racket/draw)
(require slideshow)

(define *rules* '((1 1 1) (1 1 0) (1 0 1) (1 0 0)
		  (0 1 1) (0 1 0) (0 0 1) (0 0 0)))

(define (bordered-square n)
  (filled-rectangle n n #:draw-border? #t))

(define (draw-row lst)
  (apply hc-append 2 (map (λ (x) (colorize (bordered-square 10) (cond ((= x 0) "gray")
								      ((= x 1) "red")
								      (else "gray"))))
			  lst)))

(define (extract-neighborhood nth prev-row)
  (take (drop (append '(0) prev-row '(0)) nth) 3))

(define (automaton-to-bits n)
  (reverse (map (λ (y) (if (zero? (bitwise-and y n)) 0 1))
		(map (λ (x) (expt 2 x)) (range 0 8)))))

(define (get-rules bits)
  (map cdr (filter (λ (x) (= (car x) 1)) (map cons bits *rules*))))

(define (advance-row old-row rules)
  (let ([new '()])
    (for ([i (in-range 0 (length old-row))])
      (set! new (cons (if (member (extract-neighborhood i old-row)
				  rules) 1 0) new)))
    (reverse new)))

(define (draw-automaton automaton init-row row-number)
  (let* ([bit-representation (automaton-to-bits automaton)]
	 [rules (get-rules bit-representation)]
	 [rows (list init-row)])
    (for ([i (in-range 1 row-number)])
      (set! rows (cons (advance-row (car rows) rules)
		       rows)))
    (apply vc-append 2 (map draw-row (reverse rows)))))

(draw-automaton 104 '(0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0) 10)
```



## REXX

This REXX version will show (as a default)   40   generations,   or less if the generations of cellular automata repeat.

```rexx
/*REXX program generates & displays N generations of one─dimensional cellular automata. */
parse arg $ gens .                               /*obtain optional arguments from the CL*/
if    $=='' |    $==","  then $=001110110101010  /*Not specified?  Then use the default.*/
if gens=='' | gens==","  then gens=40            /* "      "         "   "   "     "    */

   do #=0  for gens                              /* process the  one-dimensional  cells.*/
   say  " generation"    right(#,length(gens))       ' '       translate($, "#·", 10)
   @=0                                                                /* [↓] generation.*/
          do j=2  for length($) - 1;          x=substr($, j-1, 3)     /*obtain the cell.*/
          if x==011 | x==101 | x==110  then @=overlay(1, @, j)        /*the cell lives. */
                                       else @=overlay(0, @, j)        /* "   "    dies. */
          end   /*j*/

   if $==@  then do;  say right('repeats', 40);  leave;  end          /*does it repeat? */
   $=@                                           /*now use the next generation of cells.*/
   end       /*#*/                               /*stick a fork in it,  we're all done. */
```

'''output''' when using the default input:

```txt

 generation  0   ··###·##·#·#·#·
 generation  1   ··#·#####·#·#··
 generation  2   ···##···##·#···
 generation  3   ···##···###····
 generation  4   ···##···#·#····
 generation  5   ···##····#·····
 generation  6   ···##··········
                                 repeats

```



## Retro


```Retro
# 1D Cellular Automota

Assume an array of cells with an initial distribution of live and
dead cells, and imaginary cells off the end of the array having
fixed values.

Cells in the next generation of the array are calculated based on
the value of the cell and its left and right nearest neighbors in
the current generation.

If, in the following table, a live cell is represented by 1 and a
dead cell by 0 then to generate the value of the cell at a particular
index in the array of cellular values you use the following table:

000 -> 0  #
001 -> 0  #
010 -> 0  # Dies without enough neighbours
011 -> 1  # Needs one neighbour to survive
100 -> 0  #
101 -> 1  # Two neighbours giving birth
110 -> 1  # Needs one neighbour to survive
111 -> 0  # Starved to death.

I had originally written an implementation of this in RETRO 11.
For RETRO 12 I took advantage of new language features and some
further considerations into the rules for this task.

The first word, `string,` inlines a string to `here`. I'll use
this to setup the initial input.

~~~
:string, (s-) [ , ] s:for-each #0 , ;
~~~

The next two lines setup an initial generation and a buffer for
the evolved generation. In this case, `This` is the current
generation and `Next` reflects the next step in the evolution.

~~~
'This d:create
  '.###.##.#.#.#.#..#.. string,

'Next d:create
  '.................... string,
~~~

I use `display` to show the current generation.

~~~
:display (-)
  &This s:put nl ;
~~~

As might be expected, `update` copies the `Next` generation to
the `This` generation, setting things up for the next cycle.

~~~
:update (-)
  &Next &This dup s:length copy ;
~~~

The word `group` extracts a group of three cells. This data will
be passed to `evolve` for processing.

~~~
:group (a-nnn)
  [ fetch ]
  [ n:inc fetch ]
  [ n:inc n:inc fetch ] tri ;
~~~

I use `evolve` to decide how a cell should change, based on its
initial state with relation to its neighbors.

In the prior implementation this part was much more complex as I
tallied things up and had separate conditions for each combination.
This time I take advantage of the fact that only cells with two
neighbors will be alive in the next generation. So the process is:

- take the data from `group`
- compare to `$#` (for living cells)
- add the flags
- if the result is `#-2`, the cell should live
- otherwise it'll be dead

~~~
:evolve (nnn-c)
  [ $# eq? ] tri@ + +
  #-2 eq? [ $# ] [ $. ] choose ;
~~~

For readability I separated out the next few things. `at` takes an
index and returns the address in `This` starting with the index.

~~~
:at (n-na)
  &This over + ;
~~~

The `record` word adds the evolved value to a buffer. In this case
my `generation` code will set the buffer to `Next`.

~~~
:record (c-)
  buffer:add n:inc ;
~~~

And now to tie it all together. Meet `generation`, the longest bit
of code in this sample. It has several bits:

- setup a new buffer pointing to `Next`

  - this also preserves the old buffer

- setup a loop for each cell in `This`

  - initial loop index at -1, to ensure proper dummy state for first cell
  - get length of `This` generation

- perform a loop for each item in the generation, updating `Next` as it goes

- copy `Next` to `This` using `update`.

~~~
:generation (-)
  [ &Next buffer:set
    #-1 &This s:length
    [ at group evolve record ] times drop
    update
  ] buffer:preserve ;
~~~

The last bit is a helper. It takes a number of generations and displays
the state, then runs a `generation`.

~~~
:generations (n-)
  [ display generation ] times ;
~~~

And a text. The output should be:

    .###.##.#.#.#.#..#..
    .#.#####.#.#.#......
    ..##...##.#.#.......
    ..##...###.#........
    ..##...#.##.........
    ..##....###.........
    ..##....#.#.........
    ..##.....#..........
    ..##................
    ..##................

~~~
#10 generations
~~~
```



## Ring


```ring

# Project : One-dimensional cellular automata

rule = ["0", "0", "0", "1", "0", "1", "1", "0"]
now = "01110110101010100100"

for generation = 0 to 9
    see "generation " + generation + ": " + now + nl
    nxt = ""
    for cell = 1 to len(now)
        str = "bintodec(" + '"' +substr("0"+now+"0", cell, 3) + '"' + ")"
        eval("p=" + str)
        nxt = nxt + rule[p+1]
    next
    temp = nxt
    nxt = now
    now = temp
next

func bintodec(bin)
     binsum = 0
     for n=1  to len(bin)
         binsum = binsum + number(bin[n]) *pow(2, len(bin)-n)
     next
     return binsum

```

Output:

```txt

generation 0: 01110110101010100100
generation 1: 01011111010101000000
generation 2: 00110001101010000000
generation 3: 00110001110100000000
generation 4: 00110001011000000000
generation 5: 00110000111000000000
generation 6: 00110000101000000000
generation 7: 00110000010000000000
generation 8: 00110000000000000000
generation 9: 00110000000000000000

```



## Ruby


```ruby
def evolve(ary)
  ([0]+ary+[0]).each_cons(3).map{|a,b,c| a+b+c == 2 ? 1 : 0}
end

def printit(ary)
  puts ary.join.tr("01",".#")
end

ary = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
printit ary
until ary == (new = evolve(ary))
  printit ary = new
end
```

{{out}}

```txt
.###.##.#.#.#.#..#..
.#.#####.#.#.#......
..##...##.#.#.......
..##...###.#........
..##...#.##.........
..##....###.........
..##....#.#.........
..##.....#..........
..##................
```



## Rust


```rust
fn get_new_state(windowed: &[bool]) -> bool {
    match windowed {
        [false, true, true] | [true, true, false] => true,
        _ => false
    }
}

fn next_gen(cell: &mut [bool]) {
    let mut v = Vec::with_capacity(cell.len());
    v.push(cell[0]);
    for i in cell.windows(3) {
        v.push(get_new_state(i));
    }
    v.push(cell[cell.len() - 1]);
    cell.copy_from_slice(&v);
}

fn print_cell(cell: &[bool]) {
    for v in cell {
        print!("{} ", if *v {'#'} else {' '});
    }
    println!();
}

fn main() {

    const MAX_GENERATION: usize = 10;
    const CELLS_LENGTH: usize = 30;

    let mut cell: [bool; CELLS_LENGTH] = rand::random();

    for i in 1..=MAX_GENERATION {
        print!("Gen {:2}: ", i);
        print_cell(&cell);
        next_gen(&mut cell);
    }
}

```



## Scala

{{works with|Scala|2.8}}

```scala
def cellularAutomata(s: String) = {
  def it = Iterator.iterate(s) ( generation =>
    ("_%s_" format generation).iterator
    sliding 3
    map (_ count (_ == '#'))
    map Map(2 -> "#").withDefaultValue("_")
    mkString
  )

  (it drop 1) zip it takeWhile Function.tupled(_ != _) map (_._2) foreach println
}
```


Sample:


```txt

scala> cellularAutomata("_###_##_#_#_#_#__#__")
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________

```



## Scheme

{{Works with|Scheme|R$^5$RS}}

```scheme
(define (next-generation left petri-dish right)
  (if (null? petri-dish)
      (list)
      (cons (if (= (+ left
                      (car petri-dish)
                      (if (null? (cdr petri-dish))
                          right
                          (cadr petri-dish)))
                   2)
                1
                0)
            (next-generation (car petri-dish) (cdr petri-dish) right))))

(define (display-evolution petri-dish generations)
  (if (not (zero? generations))
      (begin (display petri-dish)
             (newline)
             (display-evolution (next-generation 0 petri-dish 0)
                                (- generations 1)))))

(display-evolution (list 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0) 10)
```

Output:

```txt
(1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0)
(1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0)
(0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0)
(0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0)
(0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0)
(0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
```



## Seed7

A graphical cellular automaton can be found [http://seed7.sourceforge.net/algorith/graphic.htm#cellauto here].


```seed7
$ include "seed7_05.s7i";

const string: start is "_###_##_#_#_#_#__#__";

const proc: main is func
  local
    var string: g0 is start;
    var string: g1 is start;
    var integer: generation is 0;
    var integer: i is 0;
  begin
    writeln(g0);
    for generation range 0 to 9 do
      for i range 2 to pred(length(g0)) do
        if g0[i-1] <> g0[i+1] then
          g1 @:= [i] g0[i];
        elsif g0[i] = '_' then
          g1 @:= [i] g0[i-1];
        else
          g1 @:= [i] '_'
        end if;
      end for;
      writeln(g1);
      g0 := g1;
    end for;
  end func;
```


Output:

```txt

_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________

```



## SequenceL


```sequencel>import  ";

stringToCells(string(1))[i] := 0 when string[i] = '_' else 1;
cellsToString(cells(1))[i] := '#' when cells[i] = 1 else '_';

run(cellsString(1), generations) :=
        runHelper(stringToCells(cellsString), generations, cellsString);

runHelper(cells(1), generations, result(1)) :=
    let
        nextCells := step(cells);
    in
        result when generations = 0
    else
        runHelper(nextCells, generations - 1,
                  result ++ "\n" ++ cellsToString(nextCells));

step(cells(1))[i] :=
    let
        left := cells[i-1] when i > 1 else 0;
        right := cells[i + 1] when i < size(cells) else 0;
    in
        1 when (left + cells[i] + right) = 2
    else
        0;
```


{{out}}

```txt

"_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________"

```



## Sidef

{{trans|Perl}}

```ruby
var seq = "_###_##_#_#_#_#__#__";
var x = '';

loop {
    seq.tr!('01', '_#');
    say seq;
    seq.tr!('_#', '01');
    seq.gsub!(/(?<=(.))(.)(?=(.))/, {|s1,s2,s3| s1 == s3 ? (s1 ? 1-s2 : 0) : s2});
    (x != seq) && (x = seq) || break;
}
```


{{out}}

```txt

_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________

```


{{trans|Perl 6}}

```ruby
class Automaton(rule, cells) {

    method init {
        rule = sprintf("%08b", rule).chars.map{.to_i}.reverse;
    }

    method next {
        var previous = cells.map{_};
        var len = previous.len;
        cells[] = rule[
                previous.range.map { |i|
                    4*previous[i-1 % len] +
                    2*previous[i]         +
                      previous[i+1 % len]
                }...
            ]
    }

    method to_s {
        cells.map { _ ? '#' : ' ' }.join;
    }
}

var size = 10;
var auto = Automaton(
    rule: 104,
    cells: [(size/2).of(0)..., 111011010101.digits..., (size/2).of(0)...],
);

size.times {
    say "|#{auto}|";
    auto.next;
}
```


{{out}}

```txt

|     ### ## # # #     |
|     # ##### # #      |
|      ##   ## #       |
|      ##   ###        |
|      ##   # #        |
|      ##    #         |
|      ##              |
|      ##              |
|      ##              |
|      ##              |

```



## Tcl


```tcl
proc evolve {a} {
    set new [list]
    for {set i 0} {$i < [llength $a]} {incr i} {
        lappend new [fate $a $i]
    }
    return $new
}

proc fate {a i} {
    return [expr {[sum $a $i] == 2}]
}

proc sum {a i} {
    set sum 0
    set start [expr {$i - 1 < 0 ? 0 : $i - 1}]
    set end [expr {$i + 1 >= [llength $a] ? $i : $i + 1}]
    for {set j $start} {$j <= $end} {incr j} {
        incr sum [lindex $a $j]
    }
    return $sum
}

proc print {a} {
    puts [string map {0 _ 1 #} [join $a ""]]
}

proc parse {s} {
    return [split [string map {_ 0 # 1} $s] ""]
}

set array [parse "_###_##_#_#_#_#__#__"]
print $array
while {[set new [evolve $array]] ne $array} {
    set array $new
    print $array
}
```



## Ursala

Three functions are defined. Rule takes a neighborhood of three cells to the
succeeding value of the middle one, step takes a list of cells to its successor
by applying the rule across a sliding window,
and evolve takes an initial list of cells to a list of those evolving from
it according to the rule. The cells are maintained as a list of booleans
(0 and &) but are converted to characters for presentation in the example code.

```Ursala
#import std
#import nat

rule = -$<0,0,0,&,0,&,&,0>@rSS zipp0*ziD iota8

step = rule*+ swin3+ :/0+ --<0>

evolve "n" = @iNC ~&x+ rep"n" ^C/step@h ~&

#show+

example =  ~&?(`#!,`.!)** evolve10 <0,&,&,&,0,&,&,0,&,0,&,0,&,0,0,&,0,0>
```

output:

```txt

.###.##.#.#.#..#..
.#.#####.#.#......
..##...##.#.......
..##...###........
..##...#.#........
..##....#.........
..##..............
..##..............
..##..............
..##..............
..##..............
```




## Vedit macro language


This implementation writes the calculated patterns into an edit buffer, where the results can viewed and saved into a file if required. The edit buffer also acts as storage during calculations.

```vedit
IT("Gen 0: ..###.##.#.#.#.#..#.....")     // initial pattern
#9  = Cur_Col

for (#8 = 1; #8 < 10; #8++) {             // 10 generations
    Goto_Col(7)
    Reg_Empty(20)
    while (Cur_Col < #9-1) {
        if (Match("|{##|!#,#.#,|!###}")==0) {
            Reg_Set(20, "#", APPEND)
        } else {
            Reg_Set(20, ".", APPEND)
        }
        Char
    }
    EOL IN
    IT("Gen ") Num_Ins(#8, LEFT+NOCR) IT(": ")
    Reg_Ins(20)
}
```


Sample output:

```vedit
Gen 0: ..###.##.#.#.#.#..#.....
Gen 1: ..#.#####.#.#.#.........
Gen 2: ...##...##.#.#..........
Gen 3: ...##...###.#...........
Gen 4: ...##...#.##............
Gen 5: ...##....###............
Gen 6: ...##....#.#............
Gen 7: ...##.....#.............
Gen 8: ...##...................
Gen 9: ...##...................
```



## Visual Basic .NET


This implementation is run from the command line.  The command is followed by a string of either 1's or #'s for an active cell, or 0's or _'s for an inactive one.


```Visual Basic .NET
Imports System.Text

Module CellularAutomata

    Private Enum PetriStatus
        Active
        Stable
        Dead
    End Enum

    Function Main(ByVal cmdArgs() As String) As Integer
        If cmdArgs.Length = 0 Or cmdArgs.Length > 1 Then
            Console.WriteLine("Command requires string of either 1s and 0s or #s and _s.")
            Return 1
        End If

        Dim petriDish As BitArray

        Try
            petriDish = InitialisePetriDish(cmdArgs(0))
        Catch ex As Exception
            Console.WriteLine(ex.Message)
            Return 1
        End Try

        Dim generation As Integer = 0
        Dim ps As PetriStatus = PetriStatus.Active

        Do While True
            If ps = PetriStatus.Stable Then
                Console.WriteLine("Sample stable after {0} generations.", generation - 1)
                Exit Do
            Else
                Console.WriteLine("{0}: {1}", generation.ToString("D3"), BuildDishString(petriDish))
                If ps = PetriStatus.Dead Then
                    Console.WriteLine("Sample dead after {0} generations.", generation)
                    Exit Do
                End If
            End If

            ps = GetNextGeneration(petriDish)
            generation += 1
        Loop

        Return 0
    End Function

    Private Function InitialisePetriDish(ByVal Sample As String) As BitArray
        Dim PetriDish As New BitArray(Sample.Length)
        Dim dead As Boolean = True

        For i As Integer = 0 To Sample.Length - 1
            Select Case Sample.Substring(i, 1)
                Case "1", "#"
                    PetriDish(i) = True
                    dead = False
                Case "0", "_"
                    PetriDish(i) = False
                Case Else
                    Throw New Exception("Illegal value in string position " & i)
                    Return Nothing
            End Select
        Next

        If dead Then
            Throw New Exception("Entered sample is dead.")
            Return Nothing
        End If

        Return PetriDish
    End Function

    Private Function GetNextGeneration(ByRef PetriDish As BitArray) As PetriStatus
        Dim petriCache = New BitArray(PetriDish.Length)
        Dim neighbours As Integer
        Dim stable As Boolean = True
        Dim dead As Boolean = True

        For i As Integer = 0 To PetriDish.Length - 1
            neighbours = 0
            If i > 0 AndAlso PetriDish(i - 1) Then neighbours += 1
            If i < PetriDish.Length - 1 AndAlso PetriDish(i + 1) Then neighbours += 1

            petriCache(i) = (PetriDish(i) And neighbours = 1) OrElse (Not PetriDish(i) And neighbours = 2)
            If PetriDish(i) <> petriCache(i) Then stable = False
            If petriCache(i) Then dead = False
        Next

        PetriDish = petriCache

        If dead Then Return PetriStatus.Dead
        If stable Then Return PetriStatus.Stable
        Return PetriStatus.Active

    End Function

    Private Function BuildDishString(ByVal PetriDish As BitArray) As String
        Dim sw As New StringBuilder()
        For Each b As Boolean In PetriDish
            sw.Append(IIf(b, "#", "_"))
        Next

        Return sw.ToString()
    End Function
End Module
```


Output:

```txt
C:\>CellularAutomata _###_##_#_#_#_#__#__
000: _###_##_#_#_#_#__#__
001: _#_#####_#_#_#______
002: __##___##_#_#_______
003: __##___###_#________
004: __##___#_##_________
005: __##____###_________
006: __##____#_#_________
007: __##_____#__________
008: __##________________
Sample stable after 8 generations.
```



## Wart


### Simple


```python
def (gens n l)
  prn l
  repeat n
    zap! gen l
    prn l

def (gen l)
  with (a nil  b nil  c l.0)
    collect nil  # won't insert paren without second token
      each x cdr.l
        shift! a b c x
        yield (next a b c)
      yield (next b c nil)

def (next a b c)  # next state of b given neighbors a and c
  if (and a c)  not.b
     (or a c)  b
```


Output looks a little ugly:


```txt
ready! type in an expression, then hit enter twice. ctrl-d exits.
gens 5 '(1 1 1 nil 1)

(1 1 1 nil 1)
(1 nil 1 1 nil)
(nil 1 1 1 nil)
(nil 1 nil 1 nil)
(nil nil 1 nil nil)
(nil nil nil nil nil)
```



### More sophisticated

Computing the next generation becomes much cleaner once you invest a few LoC in a new datatype.


```python
def (uca l)  # new datatype: Uni-dimensional Cellular Automaton
  (tag uca (list l len.l))

def (len l) :case (isa uca l)  # how to compute its length
  rep.l.1

defcoerce uca list  # how to convert it to a list
  (fn(_) rep._.0)

def (pr l) :case (isa uca l)  # how to print it
  each x l  # transparently coerces to a list for iterating over
    pr (if x "#" "_")

# (l i) returns ith cell when l is a uca, and nil when i is out-of-bounds
defcall uca (l i)
  if (0 <= i < len.l)
    rep.l.0.i

def (gens n l)
  prn l
  repeat n
    zap! gen l
    prn l

def (gen l)
  uca+collect+for i 0 (i < len.l) ++i
    yield (next  (l i-1)  l.i  (l i+1))

# next state of b, given neighbors a and c
def (next a b c)
  if (and a c) not.b
     (or a c)  b
```


Output is prettier now:


```txt
ready! type in an expression, then hit enter twice. ctrl-d exits.
gens 10 (uca '(nil 1 1 1 nil 1 1 nil 1 nil 1 nil 1 nil 1 nil nil 1 nil nil))

_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________
```



## XPL0


```XPL0
code ChOut=8, CrLf=9;
int  Gen, Now, New, I;
[Now:= $076A_A400;
for Gen:= 1 to 10 do
    [for I:= 31 downto 0 do ChOut(0, if Now & 1<>(I-1) & 7 of %011, %101, %110: New:= New ! 1<L(False,True,True,True,False...)
do(10){ cells.apply(chars.get).concat().println(); cells=life1D(cells); }
```

Or, using strings instead of lists:

```zkl
fcn life1D(line){
   right:=line[1,*] + "_";  // shift left, "_" fill
   left :="_" + line[0,-1]; // shift right
   Utils.Helpers.zipWith(
      fcn(a,b,c){ (String(a,b,c) - "_") == "##" and "#" or "_" },
      left,line,right).concat();
}
```


```zkl
cells:="_###_##_#_#_#_#__#__";
do(10){ cells.println(); cells=life1D(cells); }
```

{{out}}

```txt

_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________

```

/pre>


## Seed7

A graphical cellular automaton can be found [http://seed7.sourceforge.net/algorith/graphic.htm#cellauto here].

> petriCache(i) Then stable = False
            If petriCache(i) Then dead = False
        Next

        PetriDish = petriCache

        If dead Then Return PetriStatus.Dead
        If stable Then Return PetriStatus.Stable
        Return PetriStatus.Active

    End Function

    Private Function BuildDishString(ByVal PetriDish As BitArray) As String
        Dim sw As New StringBuilder()
        For Each b As Boolean In PetriDish
            sw.Append(IIf(b, "#", "_"))
        Next

        Return sw.ToString()
    End Function
End Module