One-dimensional cellular automata
You are encouraged to solve this task according to the task description, using any language you may know.
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 neighbours 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.
8th
<lang forth> \ one-dimensional automaton
\ direct map of input state to output state: {
" " : 32, " #" : 32, " # " : 32, " ##" : 35, "# " : 32, "# #" : 35, "## " : 35, "###" : 32,
} var, lifemap
- transition \ s ix (r:s') -- (r:s')
>r dup r@ n:1- 3 s:slice lifemap @ swap caseof r> swap r@ -rot s:! >r ;
\ run over 'state' and generate new state
- gen \ s -- s'
clone >r dup s:len 2 n:- ' transition 1 rot loop drop r> ;
- life \ s -- s'
dup . cr gen ;
" ### ## # # # # # " ' life 10 times bye
</lang>
ACL2
<lang lisp>(defun rc-step-r (cells)
(if (endp (rest cells))
nil
(cons (if (second cells)
(xor (first cells) (third cells))
(and (first cells) (third cells)))
(rc-step-r (rest cells)))))
(defun rc-step (cells)
(cons (and (first cells) (second cells))
(rc-step-r cells)))
(defun rc-steps-r (cells n prev)
(declare (xargs :measure (nfix n)))
(if (or (zp n) (equal cells prev))
nil
(let ((new (rc-step cells)))
(cons new (rc-steps-r new (1- n) cells)))))
(defun rc-steps (cells n)
(cons cells (rc-steps-r cells n nil)))
(defun pretty-row (row)
(if (endp row)
(cw "~%")
(prog2$ (cw (if (first row) "#" "-"))
(pretty-row (rest row)))))
(defun pretty-output (out)
(if (endp out)
nil
(prog2$ (pretty-row (first out))
(pretty-output (rest out)))))</lang>
Ada
<lang ada>with Ada.Text_IO; use Ada.Text_IO;
procedure Cellular_Automata is
type Petri_Dish is array (Positive range <>) of Boolean;
procedure Step (Culture : in out Petri_Dish) is
Left : Boolean := False;
This : Boolean;
Right : Boolean;
begin
for Index in Culture'First..Culture'Last - 1 loop
Right := Culture (Index + 1);
This := Culture (Index);
Culture (Index) := (This and (Left xor Right)) or (not This and Left and Right);
Left := This;
end loop;
Culture (Culture'Last) := Culture (Culture'Last) and not Left;
end Step;
procedure Put (Culture : Petri_Dish) is
begin
for Index in Culture'Range loop
if Culture (Index) then
Put ('#');
else
Put ('_');
end if;
end loop;
end Put;
Culture : Petri_Dish :=
( False, True, True, True, False, True, True, False, True, False, True,
False, True, False, True, False, False, True, False, False
);
begin
for Generation in 0..9 loop
Put ("Generation" & Integer'Image (Generation) & ' ');
Put (Culture);
New_Line;
Step (Culture);
end loop;
end Cellular_Automata;</lang>
The implementation defines Petri dish type with Boolean items identifying whether a place is occupied by a living cell. State transition is determined by a simple Boolean expression of three arguments.
- Output:
Generation 0 _###_##_#_#_#_#__#__ Generation 1 _#_#####_#_#_#______ Generation 2 __##___##_#_#_______ Generation 3 __##___###_#________ Generation 4 __##___#_##_________ Generation 5 __##____###_________ Generation 6 __##____#_#_________ Generation 7 __##_____#__________ Generation 8 __##________________ Generation 9 __##________________
ALGOL 68
Using the low level packed arrays of BITS manipulation operators
<lang algol68>INT stop generation = 9; INT universe width = 20; FORMAT alive or dead = $b("#","_")$;
BITS universe := 2r01110110101010100100;
# universe := BIN ( ENTIER ( random * max int ) ); #
INT upb universe = bits width; INT lwb universe = bits width - universe width + 1;
PROC couple = (BITS parent, INT lwb, upb)BOOL: (
SHORT INT sum := 0; FOR bit FROM lwb TO upb DO sum +:= ABS (bit ELEM parent) OD; sum = 2
);
FOR generation FROM 0 WHILE
printf(($"Generation "d": "$, generation,
$f(alive or dead)$, []BOOL(universe)[lwb universe:upb universe],
$l$));
- WHILE # generation < stop generation DO
BITS next universe := 2r0;
# process the first event horizon manually #
IF couple(universe,lwb universe,lwb universe + 1) THEN
next universe := 2r10
FI;
# process the middle kingdom in a loop #
FOR bit FROM lwb universe + 1 TO upb universe - 1 DO
IF couple(universe,bit-1,bit+1) THEN
next universe := next universe OR 2r1
FI;
next universe := next universe SHL 1
OD;
# process the last event horizon manually # IF couple(universe, upb universe - 1, upb universe) THEN next universe := next universe OR 2r1 FI; universe := next universe
OD</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Using high level BOOL arrays
<lang algol68>INT stop generation = 9; <lang algol68>INT stop generation = 9; INT upb universe = 20; FORMAT alive or dead = $b("#","_")$;
BITS bits universe := 2r01110110101010100100;
# bits universe := BIN ( ENTIER ( random * max int ) ); #
[upb universe] BOOL universe := []BOOL(bits universe)[bits width - upb universe + 1:];
PROC couple = (REF[]BOOL parent)BOOL: (
SHORT INT sum := 0; FOR bit FROM LWB parent TO UPB parent DO sum +:= ABS (parent[bit]) OD; sum = 2
);
FOR generation FROM 0 WHILE
printf(($"Generation "d": "$, generation,
$f(alive or dead)$, universe,
$l$));
- WHILE # generation < stop generation DO
[UPB universe]BOOL next universe; # process the first event horizon manually # next universe[1] := couple(universe[:2]); # process the middle kingdom in a loop # FOR bit FROM LWB universe + 1 TO UPB universe - 1 DO next universe[bit] := couple(universe[bit-1:bit+1]) OD;
# process the last event horizon manually # next universe[UPB universe] := couple(universe[UPB universe - 1: ]); universe := next universe
OD</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
AutoHotkey
ahk discussion <lang autohotkey>n := 22, n1 := n+1, v0 := v%n1% := 0 ; set grid dimensions, and fixed cells
Loop % n { ; draw a line of checkboxes
v%A_Index% := 0 Gui Add, CheckBox, % "y10 w17 h17 gCheck x" A_Index*17-5 " vv" A_Index
} Gui Add, Button, x+5 y6, step ; button to step to next generation Gui Show Return
Check:
GuiControlGet %A_GuiControl% ; set cells by the mouse
Return
ButtonStep: ; move to next generation
Loop % n
i := A_Index-1, j := i+2, w%A_Index% := v%i%+v%A_Index%+v%j% = 2
Loop % n
GuiControl,,v%A_Index%, % v%A_Index% := w%A_Index%
Return
GuiClose: ; exit when GUI is closed ExitApp</lang>
AWK
<lang awk>#!/usr/bin/awk -f BEGIN {
edge = 1
ruleNum = 104 # 01101000
maxGen = 9
mark = "@"
space = "."
initialState = ".@@@.@@.@.@.@.@..@.."
width = length(initialState)
delete rules
delete state
initRules(ruleNum)
initState(initialState, mark)
for (g = 0; g < maxGen; g++) {
showState(g, mark, space)
nextState()
}
showState(g, mark, space)
}
function nextState( newState, i, n) {
delete newState
for (i = 1; i < width - 1; i++) {
n = getRuleNum(i)
newState[i] = rules[n]
}
for (i = 0; i < width; i++) { # copy, can't assign arrays
state[i] = newState[i]
}
}
- Convert a three cell neighborhood from binary to decimal
function getRuleNum(i, rn, j, p) {
rn = 0
for (j = -1; j < 2; j++) {
p = i + j
rn = rn * 2 + (p < 0 || p > width ? edge : state[p])
}
return rn
}
function showState(gen, mark, space, i) {
printf("%3d: ", gen)
for (i = 1; i <= width; i++) {
printf(" %s", (state[i] ? mark : space))
}
print ""
}
- Make state transition lookup table from rule number.
function initRules(ruleNum, i, r) {
delete rules;
r = ruleNum
for (i = 0; i < 8; i++) {
rules[i] = r % 2
r = int(r / 2)
}
}
function initState(init, mark, i) {
delete state
srand()
for (i = 0; i < width; i++) {
state[i] = (substr(init, i, 1) == mark ? 1 : 0) # Given an initial string.
# state[int(width/2)] = '@' # middle cell
# state[i] = int(rand() * 100) < 30 ? 1 : 0 # 30% of cells
}
} </lang>
- Output:
0: . @ @ @ . @ @ . @ . @ . @ . @ . . @ . . 1: . @ . @ @ @ @ @ . @ . @ . @ . . . . . . 2: . . @ @ . . . @ @ . @ . @ . . . . . . . 3: . . @ @ . . . @ @ @ . @ . . . . . . . . 4: . . @ @ . . . @ . @ @ . . . . . . . . . 5: . . @ @ . . . . @ @ @ . . . . . . . . . 6: . . @ @ . . . . @ . @ . . . . . . . . . 7: . . @ @ . . . . . @ . . . . . . . . . . 8: . . @ @ . . . . . . . . . . . . . . . . 9: . . @ @ . . . . . . . . . . . . . . . .
BASIC
<lang qbasic>DECLARE FUNCTION life$ (lastGen$) DECLARE FUNCTION getNeighbors! (group$) CLS start$ = "_###_##_#_#_#_#__#__" numGens = 10 FOR i = 0 TO numGens - 1 PRINT "Generation"; i; ": "; start$ start$ = life$(start$) NEXT i
FUNCTION getNeighbors (group$) ans = 0 IF (MID$(group$, 1, 1) = "#") THEN ans = ans + 1 IF (MID$(group$, 3, 1) = "#") THEN ans = ans + 1 getNeighbors = ans END FUNCTION
FUNCTION life$ (lastGen$) newGen$ = "" FOR i = 1 TO LEN(lastGen$) neighbors = 0 IF (i = 1) THEN 'left edge IF MID$(lastGen$, 2, 1) = "#" THEN neighbors = 1 ELSE neighbors = 0 END IF ELSEIF (i = LEN(lastGen$)) THEN 'right edge IF MID$(lastGen$, LEN(lastGen$) - 1, 1) = "#" THEN neighbors = 1 ELSE neighbors = 0 END IF ELSE 'middle neighbors = getNeighbors(MID$(lastGen$, i - 1, 3)) END IF
IF (neighbors = 0) THEN 'dies or stays dead with no neighbors newGen$ = newGen$ + "_" END IF IF (neighbors = 1) THEN 'stays with one neighbor newGen$ = newGen$ + MID$(lastGen$, i, 1) END IF IF (neighbors = 2) THEN 'flips with two neighbors IF MID$(lastGen$, i, 1) = "#" THEN newGen$ = newGen$ + "_" ELSE newGen$ = newGen$ + "#" END IF END IF NEXT i life$ = newGen$ END FUNCTION</lang>
- Output:
Generation 0 : _###_##_#_#_#_#__#__ Generation 1 : _#_#####_#_#_#______ Generation 2 : __##___##_#_#_______ Generation 3 : __##___###_#________ Generation 4 : __##___#_##_________ Generation 5 : __##____###_________ Generation 6 : __##____#_#_________ Generation 7 : __##_____#__________ Generation 8 : __##________________ Generation 9 : __##________________
Batch File
This implementation will not stop showing generations, unless the cellular automata is already stable. <lang dos>@echo off setlocal enabledelayedexpansion
- THE MAIN THING
call :one-dca __###__##_#_##_###__######_###_#####_#__##_____#_#_#######__ pause>nul exit /b
- /THE MAIN THING
- THE PROCESSOR
- one-dca
echo.&set numchars=0&set proc=%1
- COUNT THE NUMBER OF CHARS
set bef=%proc:_=_,% set bef=%bef:#=#,% set bef=%bef:~0,-1% for %%x in (%bef%) do set /a numchars+=1
set /a endchar=%numchars%-1
- nextgen
echo. ^| %proc% ^| set currnum=0 set newgen=
- editeachchar
set neigh=0 set /a testnum2=%currnum%+1 set /a testnum1=%currnum%-1 if %currnum%==%endchar% ( set testchar=!proc:~%testnum1%,1! if !testchar!==# (set neigh=1) ) else ( if %currnum%==0 ( set testchar=%proc:~1,1% if !testchar!==# (set neigh=1) ) else ( set testchar1=!proc:~%testnum1%,1! set testchar2=!proc:~%testnum2%,1! if !testchar1!==# (set /a neigh+=1) if !testchar2!==# (set /a neigh+=1) ) ) if %neigh%==0 (set newgen=%newgen%_) if %neigh%==1 ( set testchar=!proc:~%currnum%,1! set newgen=%newgen%!testchar! ) if %neigh%==2 ( set testchar=!proc:~%currnum%,1! if !testchar!==# (set newgen=%newgen%_) else (set newgen=%newgen%#) ) if %currnum%==%endchar% (goto :cond) else (set /a currnum+=1&goto :editeachchar)
- cond
if %proc%==%newgen% (echo.&echo ...The sample is now stable.&goto :EOF) set proc=%newgen% goto :nextgen
- /THE (LLLLLLOOOOOOOOOOOOONNNNNNNNGGGGGG.....) PROCESSOR</lang>
- Output:
| __###__##_#_##_###__######_###_#####_#__##_____#_#_#######__ |
| __#_#__###_#####_#__#____###_###___##___##______#_##_____#__ |
| ___#___#_###___##________#_###_#___##___##_______###________ |
| ________##_#___##_________##_##____##___##_______#_#________ |
| ________###____##_________#####____##___##________#_________ |
| ________#_#____##_________#___#____##___##__________________ |
| _________#_____##__________________##___##__________________ |
| _______________##__________________##___##__________________ |
...The sample is now stable.
BBC BASIC
<lang bbcbasic> DIM rule$(7)
rule$() = "0", "0", "0", "1", "0", "1", "1", "0"
now$ = "01110110101010100100"
FOR generation% = 0 TO 9
PRINT "Generation " ; generation% ":", now$
next$ = ""
FOR cell% = 1 TO LEN(now$)
next$ += rule$(EVAL("%"+MID$("0"+now$+"0", cell%, 3)))
NEXT cell%
SWAP now$, next$
NEXT generation%</lang>
- Output:
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
Befunge
<lang befunge>v
" !!! !! ! ! ! ! ! " ,*25 <v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
" " ,*25,,,,,,,,,,,,,,,,,,,,<v
v$< @,*25,,,,,,,,,,,,,,,,,,,,<
>110p3>:1-10gg" "-4* \:10gg" "-2* \:1+10gg" "-\:54*1+`#v_20p++ :2`#v_ >:4`#v_> >$" "v
>:3`#^_v>:6`|
^ >$$$$320p10g1+:9`v > >$"!"> 20g10g1+p 20g1+:20p
^ v_10p10g
> ^</lang>
Bracmat
<lang bracmat> ( ( evolve
= n z
. @( !arg
: %?n ? @?z
: ?
( ( ( 000
| 001
| 010
| 100
| 111
)
& 0 !n:?n
| (011|101|110)
& 1 !n:?n
)
& ~`
)
?
)
| rev$(str$(!z !n))
)
& 11101101010101001001:?S
& :?seen
& whl
' ( ~(!seen:? !S ?)
& out$!S
& !S !seen:?seen
& evolve$!S:?S
)
);</lang>
- Output:
11101101010101001001 10111110101010000001 11100011010100000001 10100011101000000001 11000010110000000001 11000001110000000001 11000001010000000001 11000000100000000001 11000000000000000001
C
<lang c>#include <stdio.h>
- include <string.h>
char trans[] = "___#_##_";
- define v(i) (cell[i] != '_')
int evolve(char cell[], char backup[], int len) { int i, diff = 0;
for (i = 0; i < len; i++) { /* use left, self, right as binary number bits for table index */ backup[i] = trans[ v(i-1) * 4 + v(i) * 2 + v(i + 1) ]; diff += (backup[i] != cell[i]); }
strcpy(cell, backup); return diff; }
int main() { char c[] = "_###_##_#_#_#_#__#__\n", b[] = "____________________\n";
do { printf(c + 1); } while (evolve(c + 1, b + 1, sizeof(c) - 3)); return 0; }</lang>
- Output:
###_##_#_#_#_#__#__ #_#####_#_#_#______ _##___##_#_#_______ _##___###_#________ _##___#_##_________ _##____###_________ _##____#_#_________ _##_____#__________ _##________________
Similar to above, but without a backup string: <lang c>#include <stdio.h>
char trans[] = "___#_##_";
int evolve(char c[], int len) { int i, diff = 0;
- define v(i) ((c[i] & 15) == 1)
- define each for (i = 0; i < len; i++)
each c[i] = (c[i] == '#'); each c[i] |= (trans[(v(i-1)*4 + v(i)*2 + v(i+1))] == '#') << 4; each diff += (c[i] & 0xf) ^ (c[i] >> 4); each c[i] = (c[i] >> 4) ? '#' : '_';
- undef each
- undef v
return diff; }
int main() { char c[] = "_###_##_#_#_#_#__#__\n";
do { printf(c + 1); } while (evolve(c + 1, sizeof(c) - 3)); return 0; }</lang>
C++
Uses std::bitset for efficient packing of bit values. <lang Cpp>#include <iostream>
- include <bitset>
- include <string>
const int ArraySize = 20; const int NumGenerations = 10; const std::string Initial = "0011101101010101001000";
int main() {
// + 2 for the fixed ends of the array std::bitset<ArraySize + 2> array(Initial);
for(int j = 0; j < NumGenerations; ++j)
{
std::bitset<ArraySize + 2> tmpArray(array);
for(int i = ArraySize; i >= 1 ; --i)
{
if(array[i])
std::cout << "#";
else
std::cout << "_";
int val = (int)array[i-1] << 2 | (int)array[i] << 1 | (int)array[i+1];
tmpArray[i] = (val == 3 || val == 5 || val == 6);
}
array = tmpArray;
std::cout << std::endl;
}
}</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
C#
<lang csharp>using System; using System.Collections.Generic;
namespace prog { class MainClass { const int n_iter = 10; static int[] f = { 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0 };
public static void Main (string[] args) { for( int i=0; i<f.Length; i++ ) Console.Write( f[i]==0 ? "-" : "#" ); Console.WriteLine("");
int[] g = new int[f.Length]; for( int n=n_iter; n!=0; n-- ) { for( int i=1; i<f.Length-1; i++ ) { if ( (f[i-1] ^ f[i+1]) == 1 ) g[i] = f[i]; else if ( f[i] == 0 && (f[i-1] & f[i+1]) == 1 ) g[i] = 1; else g[i] = 0; } g[0] = ( (f[0] & f[1]) == 1 ) ? 1 : 0; g[g.Length-1] = ( (f[f.Length-1] & f[f.Length-2]) == 1 ) ? 1 : 0;
int[] tmp = f; f = g; g = tmp;
for( int i=0; i<f.Length; i++ ) Console.Write( f[i]==0 ? "-" : "#" ); Console.WriteLine(""); } } } }</lang>
Ceylon
<lang ceylon>shared void run() {
class Automata1D<Cell>({Cell*} data, Cell alive, Cell dead) given Cell satisfies Object {
assert(data.every((Cell element) => element == alive || element == dead));
value imaginaryFirstCell = data.first else dead; value imaginaryLastCell = data.last else dead;
value cells = Array {*data.rest.exceptLast};
function isAlive(Cell c) => c == alive; function flipped(Cell c) => c == alive then dead else alive;
shared Boolean evolve() { value buffer = Array { *cells.indexed.map((Integer->Cell element) { value index->cell = element; value left = cells[index - 1] else imaginaryFirstCell; value right = cells[index + 1] else imaginaryLastCell; if(isAlive(left) && isAlive(right)) { return flipped(cell); } if(isAlive(cell) && !isAlive(left) && !isAlive(right)) { return dead; } return cell; } )}; value changed = buffer != cells; buffer.copyTo(cells); return changed; }
string => imaginaryFirstCell.string + "".join(cells) + imaginaryLastCell.string; }
value automata = Automata1D("_###_##_#_#_#_#__#__", '#', '_'); variable value generation = 0; print("generation ``generation`` ``automata``"); while(automata.evolve() && generation < 10) { print("generation ``++generation`` ``automata``"); } }</lang>
Clojure
<lang clojure>(ns one-dimensional-cellular-automata
(:require (clojure.contrib (string :as s))))
(defn next-gen [cells]
(loop [cs cells ncs (s/take 1 cells)]
(let [f3 (s/take 3 cs)]
(if (= 3 (count f3))
(recur (s/drop 1 cs)
(str ncs (if (= 2 (count (filter #(= \# %) f3))) "#" "_")))
(str ncs (s/drop 1 cs))))))
(defn generate [n cells]
(if (= n 0) '() (cons cells (generate (dec n) (next-gen cells)))))
</lang> <lang clojure>one-dimensional-cellular-automata> (doseq [cells (generate 9 "_###_##_#_#_#_#__#__")]
(println cells))
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ nil </lang>
Another way:
<lang clojure>#!/usr/bin/env lein-exec
(require '[clojure.string :as str])
(def first-genr "_###_##_#_#_#_#__#__")
(def hospitable #{"_##"
"##_"
"#_#"})
(defn compute-next-genr
[genr]
(let [genr (str "_" genr "_")
groups (map str/join (partition 3 1 genr))
next-genr (for [g groups]
(if (hospitable g) \# \_))]
(str/join next-genr)))
- ---------------- main -----------------
(loop [g first-genr
i 0]
(if (not= i 10)
(do (println g)
(recur (compute-next-genr g)
(inc i)))))</lang>
Yet another way, easier to understand
<lang clojure> (def rules
{
[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
})
(defn nextgen [gen]
(concat [0]
(->> gen
(partition 3 1)
(map vec)
(map rules))
[0]))
- Output time!
(doseq [g (take 10 (iterate nextgen [0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0]))]
(println g))
</lang>
COBOL
<lang cobol>
Identification division. Program-id. rc-1d-cell. Data division. Working-storage section.
- > "Constants."
01 max-gens pic 999 value 9. 01 state-width pic 99 value 20. 01 state-table-init pic x(20) value ".@@@.@@.@.@.@.@..@..". 01 alive pic x value "@". 01 dead pic x value ".".
- > The current state.
01 state-gen pic 999 value 0.
01 state-row.
05 state-row-gen pic zz9.
05 filler pic xx value ": ".
05 state-table.
10 state-cells pic x occurs 20 times.
- > The new state.
01 new-state-table. 05 new-state-cells pic x occurs 20 times.
- > Pointer into cell table during generational production.
01 cell-index pic 99. 88 at-beginning value 1. 88 is-inside values 2 thru 19. 88 at-end value 20.
- > The cell's neighborhood.
01 neighbor-count-def.
03 neighbor-count pic 9.
88 is-comfy value 1.
88 is-ripe value 2.
Procedure division.
Perform Init-state-table.
Perform max-gens times
perform Display-row
perform Next-state
end-perform.
Perform Display-row.
Stop run.
Display-row.
Move state-gen to state-row-gen.
Display state-row.
- > Determine who lives and who dies.
Next-state.
Add 1 to state-gen.
Move state-table to new-state-table.
Perform with test after
varying cell-index from 1 by 1
until at-end
perform Count-neighbors
perform Die-off
perform New-births
end-perform
move new-state-table to state-table.
- > Living cell with wrong number of neighbors...
Die-off.
if state-cells(cell-index) =
alive and not is-comfy
then move dead to new-state-cells(cell-index)
end-if
.
- > Empty cell with exactly two neighbors are...
New-births.
if state-cells(cell-index) = dead and is-ripe
then move alive to new-state-cells(cell-index)
end-if
.
- > How many living neighbors does a cell have?
Count-neighbors.
Move 0 to neighbor-count
if at-beginning or at-end then
add 1 to neighbor-count
else
if is-inside and state-cells(cell-index - 1) = alive
then
add 1 to neighbor-count
end-if
if is-inside and state-cells(cell-index + 1) = alive
then
add 1 to neighbor-count
end-if
end-if
.
- > String is easier to enter, but table is easier to work with,
- > so move each character of the initialization string to the
- > state table.
Init-state-table.
Perform with test after
varying cell-index from 1 by 1
until at-end
move state-table-init(cell-index:1)
to state-cells(cell-index)
end-perform
.
</lang>
- Output:
0: .@@@.@@.@.@.@.@..@.. 1: .@.@@@@@.@.@.@...... 2: ..@@...@@.@.@....... 3: ..@@...@@@.@........ 4: ..@@...@.@@......... 5: ..@@....@@@......... 6: ..@@....@.@......... 7: ..@@.....@.......... 8: ..@@................ 9: ..@@................
CoffeeScript
<lang coffeescript>
- We could cheat and count the bits, but let's keep this general.
- . = dead, # = alive, middle cells survives iff one of the configurations
- below is satisified.
survival_scenarios = [
'.##' # happy neighbors '#.#' # birth '##.' # happy neighbors
]
b2c = (b) -> if b then '#' else '.'
cell_next_gen = (left_alive, me_alive, right_alive) ->
fingerprint = b2c(left_alive) + b2c(me_alive) + b2c(right_alive) fingerprint in survival_scenarios
cells_for_next_gen = (cells) ->
# This function assumes a finite array, i.e. cells can't be born outside # the original array. (cell_next_gen(cells[i-1], cells[i], cells[i+1]) for i in [0...cells.length])
display = (cells) ->
(b2c(is_alive) for is_alive in cells).join
simulate = (cells) ->
while true console.log display cells new_cells = cells_for_next_gen cells break if display(cells) == display(new_cells) cells = new_cells console.log "equilibrium achieved"
simulate (c == '#' for c in ".###.##.#.#.#.#..#..") </lang>
- Output:
> coffee cellular_automata.coffee .###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ equilibrium achieved
Common Lisp
Based upon the Ruby version. <lang lisp>(defun value (x)
(assert (> (length x) 1)) (coerce x 'simple-bit-vector))
(defun count-neighbors-and-self (value i)
(flet ((ref (i)
(if (array-in-bounds-p value i)
(bit value i)
0)))
(declare (inline ref))
(+ (ref (1- i))
(ref i)
(ref (1+ i)))))
(defun next-cycle (value)
(let ((new-value (make-array (length value) :element-type 'bit)))
(loop for i below (length value)
do (setf (bit new-value i)
(if (= 2 (count-neighbors-and-self value i))
1
0)))
new-value))
(defun print-world (value &optional (stream *standard-output*))
(loop for i below (length value)
do (princ (if (zerop (bit value i)) #\. #\#)
stream))
(terpri stream))</lang>
<lang lisp>CL-USER> (loop for previous-value = nil then value
for value = #*01110110101010100100 then (next-cycle value)
until (equalp value previous-value)
do (print-world value))
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................</lang>
D
<lang d>void main() {
import std.stdio, std.algorithm;
enum nGenerations = 10; enum initial = "0011101101010101001000"; enum table = "00010110";
char[initial.length + 2] A = '0', B = '0';
A[1 .. $-1] = initial;
foreach (immutable _; 0 .. nGenerations) {
foreach (immutable i; 1 .. A.length - 1) {
write(A[i] == '0' ? '_' : '#');
const val = (A[i-1]-'0' << 2) | (A[i]-'0' << 1) | (A[i+1]-'0');
B[i] = table[val];
}
A.swap(B);
writeln;
}
}</lang>
- Output:
__###_##_#_#_#_#__#___ __#_#####_#_#_#_______ ___##___##_#_#________ ___##___###_#_________ ___##___#_##__________ ___##____###__________ ___##____#_#__________ ___##_____#___________ ___##_________________ ___##_________________
Alternative Version
<lang d>void main() {
import std.stdio, std.algorithm, std.range;
auto A = "_###_##_#_#_#_#__#__".map!q{a == '#'}.array;
auto B = A.dup;
do {
A.map!q{ "_#"[a] }.writeln;
A.zip(A.cycle.drop(1), A.cycle.drop(A.length - 1))
.map!(t => [t[]].sum == 2).copy(B);
A.swap(B);
} while (A != B);
}</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
Alternative Version II
This version saves memory representing the state in an array of bits. For a higher performance a SWAR approach should be tried.
<lang d>void main() {
import std.stdio, std.algorithm, std.range, std.bitmanip;
immutable initial = "__###_##_#_#_#_#__#___"; enum nGenerations = 10; BitArray A, B; A.init(initial.map!(c => c == '#').array); B.length = initial.length;
foreach (immutable _; 0 .. nGenerations) {
//A.map!(b => b ? '#' : '_').writeln;
//foreach (immutable i, immutable b; A) {
foreach (immutable i; 1 .. A.length - 1) {
"_#"[A[i]].write;
immutable val = (uint(A[i - 1]) << 2) |
(uint(A[i]) << 1) |
uint(A[i + 1]);
B[i] = val == 3 || val == 5 || val == 6;
}
writeln;
A.swap(B);
}
}</lang> The output is the same as the second version.
Déjà Vu
<lang dejavu>new-state size: 0 ] repeat size: random-range 0 2 [ 0
update s1 s2: for i range 1 - len s1 2: s1! -- i s1! i s1! ++ i + + set-to s2 i = 2 s2 s1
print-state s: for i range 1 - len s 2: !print\ s! i !print ""
same-state s1 s2: for i range 1 - len s1 2: if /= s1! i s2! i: return false true
run size: new-state size new-state size while true: update print-state over if same-state over over: return print-state drop
run 60</lang>
- Output:
001110011010110111001111110111011111010011000001010111111100 001010011101111101001000011101110001100011000000101100000100 000100010111000110000000010111010001100011000000011100000000 000000001101000110000000001101100001100011000000010100000000 000000001110000110000000001111100001100011000000001000000000 000000001010000110000000001000100001100011000000000000000000 000000000100000110000000000000000001100011000000000000000000 000000000000000110000000000000000001100011000000000000000000 000000000000000110000000000000000001100011000000000000000000
DWScript
<lang delphi>const ngenerations = 10; const table = [0, 0, 0, 1, 0, 1, 1, 0];
var a := [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]; var b := a;
var i, j : Integer; for i := 1 to ngenerations do begin
for j := a.low+1 to a.high-1 do begin
if a[j] = 0 then
Print('_')
else Print('#');
var val := (a[j-1] shl 2) or (a[j] shl 1) or a[j+1];
b[j] := table[val];
end;
var tmp := a;
a := b;
b := tmp;
PrintLn();
end; </lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
E
<lang e>def step(state, rule) {
var result := state(0, 1) # fixed left cell
for i in 1..(state.size() - 2) {
# Rule function receives the substring which is the neighborhood
result += E.toString(rule(state(i-1, i+2)))
}
result += state(state.size() - 1) # fixed right cell
return result
}
def play(var state, rule, count, out) {
out.print(`0 | $state$\n`)
for i in 1..count {
state := step(state, rosettaRule)
out.print(`$i | $state$\n`)
}
return state
}</lang>
<lang e>def rosettaRule := [
" " => " ", " #" => " ", " # " => " ", " ##" => "#", "# " => " ", "# #" => "#", "## " => "#", "###" => " ",
].get
? play(" ### ## # # # # # ", rosettaRule, 9, stdout) 0 | ### ## # # # # # 1 | # ##### # # # 2 | ## ## # # 3 | ## ### # 4 | ## # ## 5 | ## ### 6 | ## # # 7 | ## # 8 | ## 9 | ##
- value: " ## "</lang>
Eiffel
<lang Eiffel> class APPLICATION
create make
feature
make -- First 10 states of the cellular automata. local r: RANDOM automata: STRING do create r.make create automata.make_empty across 1 |..| 10 as c loop if r.double_item < 0.5 then automata.append ("0") else automata.append ("1") end r.forth end across 1 |..| 10 as c loop io.put_string (automata + "%N") automata := update (automata) end end
update (s: STRING): STRING -- Next state of the cellular automata 's'. require enough_states: s.count > 1 local i: INTEGER do create Result.make_empty -- Dealing with the left border. if s [1] = '1' and s [2] = '1' then Result.append ("1") else Result.append ("0") end -- Dealing with the middle cells. from i := 2 until i = s.count loop if (s [i] = '0' and (s [i - 1] = '0' or (s [i - 1] = '1' and s [i + 1] = '0'))) or ((s [i] = '1') and ((s [i - 1] = '1' and s [i + 1] = '1') or (s [i - 1] = '0' and s [i + 1] = '0'))) then Result.append ("0") else Result.append ("1") end i := i + 1 end -- Dealing with the right border. if s [s.count] = '1' and s [s.count - 1] = '1' then Result.append ("1") else Result.append ("0") end ensure has_same_length: s.count = Result.count end
end </lang>
- Output:
1011101110 0110111010 0111101100 0100111100 0000100100 0000000000 0000000000 0000000000 0000000000 0000000000
Elixir
<lang elixir>defmodule RC do
def run(list, gen \\ 0) do
print(list, gen)
next = evolve(list)
if next == list, do: print(next, gen+1), else: run(next, gen+1)
end
defp evolve(list), do: evolve(Enum.concat([[0], list, [0]]), [])
defp evolve([a,b,c], next), do: Enum.reverse([life(a,b,c) | next])
defp evolve([a,b,c|rest], next), do: evolve([b,c|rest], [life(a,b,c) | next])
defp life(a,b,c), do: (if a+b+c == 2, do: 1, else: 0)
defp print(list, gen) do
str = "Generation #{gen}: "
IO.puts Enum.reduce(list, str, fn x,s -> s <> if x==0, do: ".", else: "#" end)
end
end
RC.run([0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0])</lang>
- Output:
Generation 0: .###.##.#.#.#.#..#.. Generation 1: .#.#####.#.#.#...... Generation 2: ..##...##.#.#....... Generation 3: ..##...###.#........ Generation 4: ..##...#.##......... Generation 5: ..##....###......... Generation 6: ..##....#.#......... Generation 7: ..##.....#.......... Generation 8: ..##................ Generation 9: ..##................
Elm
<lang elm>import Maybe exposing (withDefault) import List exposing (length, tail, reverse, concat, head, append, map3) import Html exposing (Html, div, h1, text) import String exposing (join) import Svg exposing (svg) import Svg.Attributes exposing (version, width, height, viewBox,cx,cy, fill, r) import Html.App exposing (program) import Random exposing (step, initialSeed, bool, list) import Matrix exposing (fromList, mapWithLocation, flatten) -- chendrix/elm-matrix import Time exposing (Time, second, every)
type alias Model = { history : List (List Bool)
, cols : Int
, rows : Int
}
view : Model -> Html Msg view model =
let
circleInBox (row,col) value =
if value
then [ Svg.circle [ r "0.3"
, fill ("purple")
, cx (toString (toFloat col + 0.5))
, cy (toString (toFloat row + 0.5))
]
[]
]
else []
showHistory model =
model.history
|> reverse
|> fromList
|> mapWithLocation circleInBox
|> flatten
|> concat
in
div []
[ h1 [] [text "One Dimensional Cellular Automata"]
, svg [ version "1.1"
, width "700"
, height "700"
, viewBox (join " "
[ 0 |> toString
, 0 |> toString
, model.cols |> toString
, model.rows |> toString
]
)
]
(showHistory model)
]
update : Msg -> Model -> (Model, Cmd Msg) update msg model =
if length model.history == model.rows
then (model, Cmd.none)
else
let s1 = model.history |> head |> withDefault []
s0 = False :: s1
s2 = append (tail s1 |> withDefault []) [False]
gen d0 d1 d2 =
case (d0,d1,d2) of
(False, True, True) -> True
( True, False, True) -> True
( True, True, False) -> True
_ -> False
updatedHistory = map3 gen s0 s1 s2 :: model.history
updatedModel = {model | history = updatedHistory}
in (updatedModel, Cmd.none)
init : Int -> (Model, Cmd Msg) init n =
let gen1 = fst (step (list n bool) (initialSeed 34))
in ({ history = [gen1], rows = n, cols= n }, Cmd.none)
type Msg = Tick Time
subscriptions model = every (0.2 * second) Tick
main = program
{ init = init 40
, view = view
, update = update
, subscriptions = subscriptions
}</lang>
Link to live demo: https://dc25.github.io/oneDimensionalCellularAutomataElm/
Erlang
<lang erlang> -module(ca). -compile(export_all).
run(N,G) ->
run(N,G,0).
run(GN,G,GN) ->
io:fwrite("~B: ",[GN]),
print(G);
run(N,G,GN) ->
io:fwrite("~B: ",[GN]),
print(G),
run(N,next(G),GN+1).
print([]) ->
io:fwrite("~n");
print([0|T]) ->
io:fwrite("_"),
print(T);
print([1|T]) ->
io:fwrite("#"),
print(T).
next([]) ->
[];
next([_]) ->
[0];
next([H,1|_]=G) ->
next(G,[H]);
next([_|_]=G) ->
next(G,[0]).
next([],Acc) ->
lists:reverse(Acc);
next([0,_],Acc) ->
next([],[0|Acc]);
next([1,X],Acc) ->
next([],[X|Acc]);
next([0,X,0|T],Acc) ->
next([X,0|T],[0|Acc]);
next([1,X,0|T],Acc) ->
next([X,0|T],[X|Acc]);
next([0,X,1|T],Acc) ->
next([X,1|T],[X|Acc]);
next([1,0,1|T],Acc) ->
next([0,1|T],[1|Acc]);
next([1,1,1|T],Acc) ->
next([1,1|T],[0|Acc]).
</lang> Example execution: <lang erlang> 44> ca:run(9,[0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]). 0: __###_##_#_#_#_#__#___ 1: __#_#####_#_#_#_______ 2: ___##___##_#_#________ 3: ___##___###_#_________ 4: ___##___#_##__________ 5: ___##____###__________ 6: ___##____#_#__________ 7: ___##_____#___________ 8: ___##_________________ 9: ___##_________________ </lang>
ERRE
<lang ERRE> PROGRAM ONEDIM_AUTOMATA
! for rosettacode.org !
!VAR I,J,N,W,K
!$DYNAMIC DIM X[0],X2[0]
BEGIN
DATA(20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0)
PRINT(CHR$(12);)
N=20 ! number of generation required
READ(W)
!$DIM X[W+1],X2[W+1]
FOR I=1 TO W DO
READ(X[I])
END FOR
FOR K=1 TO N DO
PRINT("Generation";K;TAB(16);)
FOR J=1 TO W DO
IF X[J]=1 THEN PRINT("#";) ELSE PRINT("_";) END IF
IF X[J-1]+X[J]+X[J+1]=2 THEN X2[J]=1 ELSE X2[J]=0 END IF
END FOR
PRINT
FOR J=1 TO W DO
X[J]=X2[J]
END FOR
END FOR
END PROGRAM </lang>
- Output:
Generation 1 _###_##_#_#_#_#__#__ Generation 2 _#_#####_#_#_#______ Generation 3 __##___##_#_#_______ Generation 4 __##___###_#________ Generation 5 __##___#_##_________ Generation 6 __##____###_________ Generation 7 __##____#_#_________ Generation 8 __##_____#__________ Generation 9 __##________________ Generation 10 __##________________ Generation 11 __##________________ Generation 12 __##________________ Generation 13 __##________________ Generation 14 __##________________ Generation 15 __##________________ Generation 16 __##________________ Generation 17 __##________________ Generation 18 __##________________ Generation 19 __##________________ Generation 20 __##________________
Euphoria
<lang euphoria>include machine.e
function rules(integer tri)
return tri = 3 or tri = 5 or tri = 6
end function
function next_gen(atom gen)
atom new, bit
new = rules(and_bits(gen,3)*2) -- work with the first bit separately
bit = 2
while gen > 0 do
new += bit*rules(and_bits(gen,7))
gen = floor(gen/2) -- shift right
bit *= 2 -- shift left
end while
return new
end function
constant char_clear = '_', char_filled = '#'
procedure print_gen(atom gen)
puts(1, int_to_bits(gen,32) * (char_filled - char_clear) + char_clear) puts(1,'\n')
end procedure
function s_to_gen(sequence s)
s -= char_clear return bits_to_int(s)
end function
atom gen, prev integer n
n = 0 prev = 0 gen = bits_to_int(rand(repeat(2,32))-1) while gen != prev do
printf(1,"Generation %d: ",n) print_gen(gen) prev = gen gen = next_gen(gen) n += 1
end while
printf(1,"Generation %d: ",n) print_gen(gen)</lang>
- Output:
Generation 0: ####__#_###_#_#_#_#_##___##_##__ Generation 1: ___#___##_##_#_#_#_###___#####__ Generation 2: _______######_#_#_##_#___#___#__ Generation 3: _______#____##_#_####___________ Generation 4: ____________###_##__#___________ Generation 5: ____________#_####______________ Generation 6: _____________##__#______________ Generation 7: _____________##_________________ Generation 8: _____________##_________________
Factor
<lang factor>USING: bit-arrays io kernel locals math sequences ; IN: cellular
- bool-sum ( bool1 bool2 -- sum )
[ [ 2 ] [ 1 ] if ] [ [ 1 ] [ 0 ] if ] if ;
- neighbours ( index world -- # )
index [ 1 - ] [ 1 + ] bi [ world ?nth ] bi@ bool-sum ;
- count-neighbours ( world -- neighbours )
[ length iota ] keep [ neighbours ] curry map ;
- life-law ( alive? neighbours -- alive? )
swap [ 1 = ] [ 2 = ] if ;
- step ( world -- world' )
dup count-neighbours [ life-law ] ?{ } 2map-as ;
- print-cellular ( world -- )
[ CHAR: # CHAR: _ ? ] "" map-as print ;
- main-cellular ( -- )
?{ f t t t f t t f t f t f t f t f f t f f }
10 [ dup print-cellular step ] times print-cellular ;
MAIN: main-cellular </lang>
( scratchpad ) "cellular" run _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
Fantom
<lang fantom> class Automaton {
static Int[] evolve (Int[] array)
{
return array.map |Int x, Int i -> Int|
{
if (i == 0)
return ( (x + array[1] == 2) ? 1 : 0)
else if (i == array.size-1)
return ( (x + array[-2] == 2) ? 1 : 0)
else if (x + array[i-1] + array[i+1] == 2)
return 1
else
return 0
}
}
public static Void main ()
{
Int[] array := [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
echo (array.join(""))
Int[] newArray := evolve(array)
while (newArray != array)
{
echo (newArray.join(""))
array = newArray
newArray = evolve(array)
}
}
} </lang>
Forth
<lang forth>: init ( bits count -- )
0 do dup 1 and c, 2/ loop drop ;
20 constant size create state $2556e size init 0 c,
- .state
cr size 0 do state i + c@ if ." #" else space then loop ;
- ctable create does> + c@ ;
ctable rules $68 8 init
- gen
state c@ ( window ) size 0 do 2* state i + 1+ c@ or 7 and dup rules state i + c! loop drop ;
- life1d ( n -- )
.state 1 do gen .state loop ;
10 life1d</lang>
Fortran
<lang fortran>PROGRAM LIFE_1D
IMPLICIT NONE
LOGICAL :: cells(20) = (/ .FALSE., .TRUE., .TRUE., .TRUE., .FALSE., .TRUE., .TRUE., .FALSE., .TRUE., .FALSE., &
.TRUE., .FALSE., .TRUE., .FALSE., .TRUE., .FALSE., .FALSE., .TRUE., .FALSE., .FALSE. /)
INTEGER :: i
DO i = 0, 9
WRITE(*, "(A,I0,A)", ADVANCE = "NO") "Generation ", i, ": "
CALL Drawgen(cells)
CALL Nextgen(cells)
END DO
CONTAINS
SUBROUTINE Nextgen(cells)
LOGICAL, INTENT (IN OUT) :: cells(:)
LOGICAL :: left, centre, right
INTEGER :: i
left = .FALSE.
DO i = 1, SIZE(cells)-1
centre = cells(i)
right = cells(i+1)
IF (left .AND. right) THEN
cells(i) = .NOT. cells(i)
ELSE IF (.NOT. left .AND. .NOT. right) THEN
cells(i) = .FALSE.
END IF
left = centre
END DO
cells(SIZE(cells)) = left .AND. right
END SUBROUTINE Nextgen
SUBROUTINE Drawgen(cells)
LOGICAL, INTENT (IN OUT) :: cells(:)
INTEGER :: i
DO i = 1, SIZE(cells)
IF (cells(i)) THEN
WRITE(*, "(A)", ADVANCE = "NO") "#"
ELSE
WRITE(*, "(A)", ADVANCE = "NO") "_"
END IF
END DO
WRITE(*,*)
END SUBROUTINE Drawgen
END PROGRAM LIFE_1D</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
GFA Basic
<lang> ' ' One Dimensional Cellular Automaton ' start$="01110110101010100100" max_cycles%=20 ! give a maximum depth ' ' Global variables hold the world, with two rows ' world! is set up with 2 extra cells width, so there is a FALSE on either side ' cur% gives the row for current world, ' new% gives the row for the next world. ' size%=LEN(start$) DIM world!(size%+2,2) cur%=0 new%=1 clock%=0 ' @setup_world(start$) OPENW 1 CLEARW 1 DO
@display_world @update_world EXIT IF @same_state clock%=clock%+1 EXIT IF clock%>max_cycles% ! safety net
LOOP ~INP(2) CLOSEW 1 ' ' parse given string to set up initial states in world ' -- assumes world! is of correct size ' PROCEDURE setup_world(defn$)
LOCAL i%
' clear out the array
ARRAYFILL world!(),FALSE
' for each 1 in string, set cell to true
FOR i%=1 TO LEN(defn$)
IF MID$(defn$,i%,1)="1"
world!(i%,0)=TRUE
ENDIF
NEXT i%
' set references to cur and new
cur%=0
new%=1
RETURN ' ' Display the world ' PROCEDURE display_world
LOCAL i%
FOR i%=1 TO size%
IF world!(i%,cur%)
PRINT "#";
ELSE
PRINT ".";
ENDIF
NEXT i%
PRINT ""
RETURN ' ' Create new version of world ' PROCEDURE update_world
LOCAL i% FOR i%=1 TO size% world!(i%,new%)=@new_state(@get_value(i%)) NEXT i% ' reverse cur/new cur%=1-cur% new%=1-new%
RETURN ' ' Test if cur/new states are the same ' FUNCTION same_state
LOCAL i%
FOR i%=1 TO size%
IF world!(i%,cur%)<>world!(i%,new%)
RETURN FALSE
ENDIF
NEXT i%
RETURN TRUE
ENDFUNC ' ' Return new state of cell given value ' FUNCTION new_state(value%)
SELECT value% CASE 0,1,2,4,7 RETURN FALSE CASE 3,5,6 RETURN TRUE ENDSELECT
ENDFUNC ' ' Compute value for cell + neighbours ' FUNCTION get_value(cell%)
LOCAL result% result%=0 IF world!(cell%-1,cur%) result%=result%+4 ENDIF IF world!(cell%,cur%) result%=result%+2 ENDIF IF world!(cell%+1,cur%) result%=result%+1 ENDIF RETURN result%
ENDFUNC </lang>
Go
Sequential
<lang 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]
}
}</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
Concurrent
Computations run on each cell concurrently. Separate read and write phases. Single array of cells. <lang go>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()
}
}</lang> Output is same as sequential version.
Groovy
Solution: <lang groovy>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 }
}</lang>
Test: <lang groovy>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()}"
}</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Haskell
<lang haskell>module Life1D where
import Data.List import System.Random import Control.Monad import Control.Arrow
bnd :: [Char] -> Char bnd bs =
case bs of
"_##" -> '#'
"#_#" -> '#'
"##_" -> '#'
_ -> '_'
donxt xs = unfoldr(\xs -> case xs of [_,_] -> Nothing ;
_ -> Just (bnd $ take 3 xs, drop 1 xs)) $ '_':xs++"_"
lahmahgaan xs = init.until (liftM2 (==) last (last. init)) (ap (++)(return. donxt. last)) $ [xs, donxt xs]
main = do
g <- newStdGen
let oersoep = map ("_#"!!). take 36 $ randomRs(0,1) g
mapM_ print . lahmahgaan $ oersoep</lang>
- Output:
<lang haskell>*Life1D> mapM_ print . lahmahgaan $ "_###_##_#_#_#_#__#__" "_###_##_#_#_#_#__#__" "_#_#####_#_#_#______" "__##___##_#_#_______" "__##___###_#________" "__##___#_##_________" "__##____###_________" "__##____#_#_________" "__##_____#__________" "__##________________"
- Life1D> main
"__##_##__#____###__#__#_______#_#_##" "__#####_______#_#______________#_###" "__#___#________#________________##_#" "________________________________###_" "________________________________#_#_" "_________________________________#__" "____________________________________"</lang>
Icon and Unicon
<lang icon>
- 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 </lang>
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.
<lang unicon>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</lang>
- A couple of sample runs:
->odca 01110110101010100100 01011111010101000000 00110001101010000000 00110001110100000000 00110001011000000000 00110000111000000000 00110000101000000000 00110000010000000000 00110000000000000000 ->odca 01110110 01110110 01011110 00110010 00110000 ->
J
<lang j>life1d=: '_#'{~ (2 = 3+/\ 0,],0:)^:a:</lang>
- Example use:
<lang j> life1d ? 20 # 2 _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________</lang>
Alternative implementation:
<lang j>Rule=:2 :0 NB. , m: number of generations, n: rule number
'_#'{~ (3 ((|.n#:~8#2) {~ #.)\ 0,],0:)^:(i.m)
)</lang>
- Example use:
<lang j> 9 Rule 104 '#'='_###_##_#_#_#_#__#__' _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________</lang>
Java
This example requires a starting generation of at least length two (which is what you need for anything interesting anyway). <lang java>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; } }</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
In this version, b is replaced by a backup
which is local to the evolve method,
and the evolve method returns a boolean.
<lang java>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)); } }</lang>
- Output:
###_##_#_#_#_#__#__ #_#####_#_#_#______ _##___##_#_#_______ _##___###_#________ _##___#_##_________ _##____###_________ _##____#_#_________ _##_____#__________ _##________________
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. <lang javascript>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;
}</lang>
- Example usage:
<lang javascript>alert(caStep([0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]));</lang> 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. <lang 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 . == $prev then empty else . end) | pp;
- Example:
[0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] | go</lang>
- Output:
<lang sh>$ jq -c -r -n -f One-dimensional_cellular_automata.jq
*** ** * * * * * * ***** * * * ** ** * * ** *** * ** * ** ** *** ** * * ** * **</lang>
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. <lang Julia> function next_gen(a::BitArray{1}, isperiodic=false)
b = copy(a)
if isperiodic
ncnt = [a[end], a[1:end-1]] + [a[2:end], a[1]]
else
ncnt = [false, a[1:end-1]] + [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 = randbool(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 = randbool(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 </lang>
- Output:
A 1D Cellular Atomaton with 70 cells and empty bounds.
► ███ ██ █ ██ ███ █ ███ ██ █ █ ██████ █ ██ █ █ █ █ ██ ███ ◄
► █ █ ██ ███ █ ██ █ █ ██ █ █ ██ ███ █ █ ███ █ █ ◄
► █ ██ █ █ ███ █ ██ ██ █ ██ █ █ █ █ ◄
► ██ █ █ █ ██ ██ ████ █ ◄
► ██ █ ██ ██ █ █ ◄
► ██ ██ ██ ◄
A 1D Cellular Atomaton with 70 cells and periodic bounds.
►████ ██ █ █ █ ██ ██ █ █ ████ █ ███ ███ ██ ██ ██ ◄
►█ █ ███ █ ██ ███ █ █ █ █ █ █ ████ ██████◄
►█ █ █ ██ █ ██ █ ██ █ █ ◄
► █ ██ ███ ██ ◄
► ██ █ █ ██ ◄
► ██ █ ██ ◄
► ██ ██ ◄
K
<lang K>f:{2=+/(0,x,0)@(!#x)+/:!3}</lang>
- Example usage:
<lang K> `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________________ </lang>
Liberty BASIC
<lang lb>' [RC] 'One-dimensional cellular automata'
global rule$, state$
rule$ ="00010110" ' Rule 22 decimal
state$ ="0011101101010101001000"
for j =1 to 20
oldState$ =state$
state$ ="0"
for k =2 to 32
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
print state$
next j
end</lang>
Locomotive Basic
<lang locobasic>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</lang>
- Output:
Logo
<lang 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</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Lua
<lang 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 </lang>
- Output:
0: _###_##_#_#_#_#__#__ 1: _#_#####_#_#_#______ 2: __##___##_#_#_______ 3: __##___###_#________ 4: __##___#_##_________ 5: __##____###_________ 6: __##____#_#_________ 7: __##_____#__________ 8: __##________________ 9: __##________________
M4
<lang 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)</lang>
- 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 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Mathematica / Wolfram Language
Built-in function: <lang Mathematica>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 -> "."});</lang>
- Output:
<lang Mathematica>###.##.#.#.#.#..#
- .#####.#.#.#....
.##...##.#.#..... .##...###.#...... .##...#.##....... .##....###....... .##....#.#....... .##.....#........ .##.............. .##.............. .##.............. .##.............. .##..............</lang>
MATLAB / Octave
<lang MATLAB>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</lang>
- Output:
octave:27> one_dim_cell_automata('01110110101010100100'=='1',20);
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
__##________________
...
Modula-3
Modula-3 provides a module Word for doing bitwise operations,
but it segfaults when trying to use BOOLEAN types,
so we use INTEGER instead.
<lang modula3>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.</lang>
- Output:
Generation 0 _###_##_#_#_#_#__#__ Generation 1 _#_#####_#_#_#______ Generation 2 __##___##_#_#_______ Generation 3 __##___###_#________ Generation 4 __##___#_##_________ Generation 5 __##____###_________ Generation 6 __##____#_#_________ Generation 7 __##_____#__________ Generation 8 __##________________ Generation 9 __##________________
Nial
(life.nial) <lang 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 ]</lang>
- Using it:
<lang nial>|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</lang>
Nim
<lang Nim> import math randomize()
type
TBoolArray = array[0..30, bool] # an array that is indexed with 0..10 TSymbols = tuple[on: char , off: char]
const
num_turns = 20
symbols:TSymbols = ('#','_')
proc `==` (x:TBoolArray,y:TBoolArray): bool =
if len(x) != len(y):
return False
for i in 0..(len(x)-1):
if x[i] != y[i]:
return False
return True
proc count_neighbours(map:TBoolArray , tile:int):int =
result = 0
if tile != len(map)-1 and map[tile+1]:
result += 1
if tile != 0 and map[tile-1]:
result += 1
proc print_map(map:TBoolArray, symbols:TSymbols) =
for i in map:
if i:
write(stdout,symbols[0])
else:
write(stdout,symbols[1])
write(stdout,"\n")
proc random_map(): TBoolArray =
var map = [False,False,False,False,False,False,False,False,False,False,False,
False,False,False,False,False,False,False,False,False,False,False,
False,False,False,False,False,False,False,False,False]
for i in 0..(len(map)-1):
map[i] = bool(random(2))
return map
proc fixed_map(): TBoolArray =
var map = [False,True,True,True,False,True,True,False,True,False,True,
False,True,False,True,False,False,True,False,False,False,False,
False,False,False,False,False,False,False,False,False]
return map
- make the map
var map:TBoolArray
- map = random_map() # uncomment for random start
map = fixed_map() print_map(map,symbols) for i in 0..num_turns:
var new_map = map
for j in 0..(len(map)-1):
if map[j]:
if count_neighbours(map, j) == 2 or
count_neighbours(map, j) == 0:
new_map[j] = False
else:
if count_neighbours(map, j) == 2:
new_map[j] = True
if new_map == map:
print_map(map,symbols)
break
map = new_map
print_map(map,symbols)
</lang>
- Output:
_###_##_#_#_#_#__#_____________ _#_#####_#_#_#_________________ __##___##_#_#__________________ __##___###_#___________________ __##___#_##____________________ __##____###____________________ __##____#_#____________________ __##_____#_____________________ __##___________________________ __##___________________________
Using a string character counting method: <lang nim>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)</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
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
<lang 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()</lang>
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
<lang Oforth>: nextGen(l) | i |
StringBuffer new
l size loop: i [
l at( i 1- ) '#' ==
l at( i 1+ ) '#' == +
l at( i ) '#' == +
2 == ifTrue: [ '#' ] else: [ '_' ] over add
] ;
- gen(l, n) l dup println #[ nextGen dup println ] times(n) ;</lang>
- Output:
"_###_##_#_#_#_#__#__" 10 gen _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________ ok
Oz
<lang 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</lang>
- Output:
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. <lang 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;</lang>
Perl
Use regexp to extract and substitute cells while the string changes
Convert cells to zeros and ones to set complement state <lang perl> $_="_###_##_#_#_#_#__#__\n"; do {
y/01/_#/; print; y/_#/01/; s/(?<=(.))(.)(?=(.))/$1 == $3 ? $1 ? 1-$2 : 0 : $2/eg;
} while ($x ne $_ and $x=$_); </lang>
Use hash for complement state <lang perl> $_="_###_##_#_#_#_#__#__\n"; %h=qw(# _ _ #); do {
print;
s/(?<=(.))(.)(?=(.))/$1 eq $3 ? $1 eq "_" ? "_" : $h{$2} : $2/eg;
} while ($x ne $_ and $x=$_); </lang>
- Output:
for both versions
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
Perl 6
We'll make a general algorithm capable of computing any cellular automata as defined by Stephen Wolfram's famous book 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.
<lang perl6>class Automata {
has ($.rule, @.cells);
method gist { <| |>.join: @!cells.map({$_ ?? '#' !! ' '}).join }
method code { $.rule.fmt("%08b").comb.reverse }
method succ {
self.new: :$.rule, :cells( self.code[
[Z+] 4 «*« @.cells.rotate(-1),
2 «*« @.cells,
@.cells.rotate(1)
] )
}
}</lang>
The rule proposed for this task is rule 0b01101000 = 104
<lang perl6>my $size = 10; my Automata $a .= new:
:rule(104), :cells( 0 xx $size div 2, '111011010101'.comb, 0 xx $size div 2 );
say $a++ for ^10;</lang>
- Output:
| ### ## # # # | | # ##### # # | | ## ## # | | ## ### | | ## # # | | ## # | | ## | | ## | | ## | | ## |
Rule 104 is not particularly interesting so here is Rule 90, which shows a Sierpinski Triangle.
<lang perl6>my $size = 50; my Automata $a .= new: :rule(90), :cells( 0 xx $size div 2, 1, 0 xx $size div 2 );
say $a++ for ^20;</lang>
- Output:
| # | | # # | | # # | | # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # # # | | # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # |
Phix
Ludicrously optimised: <lang 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</lang>
- Output:
"_###_##_#_#_#_#__#__" "_#_#####_#_#_#______" "__##___##_#_#_______" "__##___###_#________" "__##___#_##_________" "__##____###_________" "__##____#_#_________" "__##_____#__________" "__##________________" "__##________________"
And of course I had to have a crack at that Sierpinski_Triangle: <lang 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</lang>
- Output:
"________________________#________________________" "_______________________#_#_______________________" "______________________#___#______________________" "_____________________#_#_#_#_____________________" "____________________#_______#____________________" "___________________#_#_____#_#___________________" "__________________#___#___#___#__________________" "_________________#_#_#_#_#_#_#_#_________________" "________________#_______________#________________" "_______________#_#_____________#_#_______________" "______________#___#___________#___#______________" "_____________#_#_#_#_________#_#_#_#_____________" "____________#_______#_______#_______#____________" "___________#_#_____#_#_____#_#_____#_#___________" "__________#___#___#___#___#___#___#___#__________" "_________#_#_#_#_#_#_#_#_#_#_#_#_#_#_#_#_________" "________#_______________________________#________" "_______#_#_____________________________#_#_______" "______#___#___________________________#___#______" "_____#_#_#_#_________________________#_#_#_#_____" "____#_______#_______________________#_______#____" "___#_#_____#_#_____________________#_#_____#_#___" "__#___#___#___#___________________#___#___#___#__" "_#_#_#_#_#_#_#_#_________________#_#_#_#_#_#_#_#_"
PicoLisp
<lang 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 "_") ) ) ) )</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
Prolog
Works ith SWI-Prolog. <lang 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 compute_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). </lang>
- Output:
?- one_dimensional_cellular_automata. .###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ true .
PureBasic
<lang 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() <> ""</lang>
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Python
Python: Straightforward interpretation of spec
<lang 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))</lang>
- Output:
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. <lang 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<<nbits)-2; endvals = 0<<(nbits+1) | 0 tr = ('____', '___#', '__#_', '__##', '_#__', '_#_#', '_##_', '_###',
'#___', '#__#', '#_#_', '#_##', '##__', '##_#', '###_', '####' )
for i in range(maxgenerations):
print "Generation %3i: %s" % (i,(.join(tr[int(t,16)] for t in (fmt%(a>>1))))) a |= endvals a = ((a&((a<<1) | (a>>1))) ^ ((a<<1)&(a>>1))) & endmask</lang>
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. <lang 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)]
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
>>> </lang>
R
<lang 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")
}</lang>
- Output:
1 _##_____####_#___#_#__ 2 _##_____#__##_____#___ 3 _##________##_________ 4 _##________##_________ 5 _##________##_________ 6 _##________##_________ 7 _##________##_________ 8 _##________##_________ 9 _##________##_________ 10 _##________##_________
Racket
<lang 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) |#</lang>
Below is an alternative implementation using graphical output in the Racket REPL. It works with DrRacket and Emacs + Geiser. <lang 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)</lang>
REXX
This REXX version will show (as a default) 40 generations, or less if the generations of cellular automata repeat. <lang 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. */</lang>
output when using the default input:
generation 0 ··###·##·#·#·#·
generation 1 ··#·#####·#·#··
generation 2 ···##···##·#···
generation 3 ···##···###····
generation 4 ···##···#·#····
generation 5 ···##····#·····
generation 6 ···##··········
repeats
Retro
<lang Retro>{{
: $, ( $- ) withLength [ @+ , ] times @ , ; create this ".###.##.#.#.#.#..#.." $, create next this getLength allot create group "..." $, variable neighbours
: reset 0 !neighbours ; : hasNeighbour? @ '# = [ neighbours ++ ] ifTrue ; : countNeighboursOnEdge '# = [ 1 ] [ 0 ] if !neighbours ; : flip dup this + @ '# = [ '. ] [ '# ] if ; : extract dup this + 1- group 3 copy ;
: count ( left ) [ 0 = ] [ @this countNeighboursOnEdge ] when ( right ) [ 19 = ] [ this 19 + @ countNeighboursOnEdge ] when ( middle ) reset extract group dup 2 + 2hasNeighbour? ;
: process reset count @neighbours [ 0 = ] [ drop dup next + '. swap ! ] when [ 1 = ] [ drop dup this + @ over next + ! ] when [ 2 = ] [ drop flip over next + ! ] when drop ;
: generation 0 this getLength [ process 1+ ] times drop next this withLength copy ;
---reveal---
: generations cr 0 swap [ [ this swap "%d %s\n" puts ] sip generation 1+ ] times drop ;
}}</lang>
Sample Output:
10 generations 0 .###.##.#.#.#.#..#.. 1 .#.#####.#.#.#...... 2 ..##...##.#.#....... 3 ..##...###.#........ 4 ..##...#.##......... 5 ..##....###......... 6 ..##....#.#......... 7 ..##.....#.......... 8 ..##................ 9 ..##................
Ruby
<lang 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</lang>
- Output:
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................
Scala
<lang 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
}</lang>
Sample:
scala> cellularAutomata("_###_##_#_#_#_#__#__")
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
Scheme
<lang 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)</lang> Output:
(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 here.
<lang 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;</lang>
Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
Sidef
<lang 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;
}</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
<lang 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;
}</lang>
- Output:
| ### ## # # # | | # ##### # # | | ## ## # | | ## ### | | ## # # | | ## # | | ## | | ## | | ## | | ## |
Tcl
<lang 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 $array
}</lang>
Ursala
Three functions are defined. Rule takes a neighborhood of three cells to the succeeding value of the middle one, step takes a list of cells to its successor by applying the rule across a sliding window, and evolve takes an initial list of cells to a list of those evolving from it according to the rule. The cells are maintained as a list of booleans (0 and &) but are converted to characters for presentation in the example code. <lang Ursala>#import std
- import nat
rule = -$<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></lang> output:
.###.##.#.#.#..#.. .#.#####.#.#...... ..##...##.#....... ..##...###........ ..##...#.#........ ..##....#......... ..##.............. ..##.............. ..##.............. ..##.............. ..##..............
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. <lang 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)
}</lang>
Sample output: <lang vedit>Gen 0: ..###.##.#.#.#.#..#..... Gen 1: ..#.#####.#.#.#......... Gen 2: ...##...##.#.#.......... Gen 3: ...##...###.#........... Gen 4: ...##...#.##............ Gen 5: ...##....###............ Gen 6: ...##....#.#............ Gen 7: ...##.....#............. Gen 8: ...##................... Gen 9: ...##...................</lang>
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.
<lang 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</lang>
Output:
C:\>CellularAutomata _###_##_#_#_#_#__#__ 000: _###_##_#_#_#_#__#__ 001: _#_#####_#_#_#______ 002: __##___##_#_#_______ 003: __##___###_#________ 004: __##___#_##_________ 005: __##____###_________ 006: __##____#_#_________ 007: __##_____#__________ 008: __##________________ Sample stable after 8 generations.
Wart
Simple
<lang 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</lang>
Output looks a little ugly:
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.
<lang python>def (uca l) # new datatype: unidim CA
(tag uca (list l len.l))
def (len l) :case (isa uca l) # how to compute its length
rep.l.1
defcoerce uca list # converting it to 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</lang>
Output is prettier now:
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
<lang 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<<I other; Now:= New; ];
]</lang>
- Output:
_____###_##_#_#_#_#__#__________ _____#_#####_#_#_#______________ ______##___##_#_#_______________ ______##___###_#________________ ______##___#_##_________________ ______##____###_________________ ______##____#_#_________________ ______##_____#__________________ ______##________________________ ______##________________________
zkl
<lang zkl>fcn life1D(line){
right:=line[1,*] + False; // shift left, False fill
left :=T(False).extend(line[0,-1]); // shift right
left.zip(line,right).apply(fcn(hood){ hood.sum(0)==2 });
}</lang> <lang zkl>chars:=T("_","#"); cells:="_###_##_#_#_#_#__#__".split("").apply('==("#")); //-->L(False,True,True,True,False...) do(10){ cells.apply(chars.get).concat().println(); cells=life1D(cells); }</lang> Or, using strings instead of lists: <lang 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();
}</lang> <lang zkl>cells:="_###_##_#_#_#_#__#__"; do(10){ cells.println(); cells=life1D(cells); }</lang>
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
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