One-dimensional cellular automata: Difference between revisions
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<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> |
<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> |
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shows an alert with "0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0". |
shows an alert with "0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0". |
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=={{header|Liberty BASIC}}== |
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<lang lb>' [RC] 'One-dimensional cellular automata' |
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global rule$, state$ |
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rule$ ="00010110" ' Rule 22 decimal |
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state$ ="0011101101010101001000" |
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for j =1 to 20 |
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oldState$ =state$ |
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state$ ="0" |
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for k =2 to 32 |
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NHood$ =mid$( oldState$, k -1, 3) ' pick 3 char neighbourhood and turn binary string to decimal |
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vNHood =0 |
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for kk =3 to 1 step -1 |
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vNHood =vNHood +val( mid$( NHood$, kk, 1)) *2^( 3 -kk) |
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next kk |
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' .... & use it to index into rule$ to find appropriate new value |
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state$ =state$ +mid$( rule$, vNHood +1, 1) |
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next k |
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print state$ |
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next j |
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end</lang> |
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=={{header|Logo}}== |
=={{header|Logo}}== |
Revision as of 03:03, 16 September 2010
![Task](http://static.miraheze.org/rosettacodewiki/thumb/b/ba/Rcode-button-task-crushed.png/64px-Rcode-button-task-crushed.png)
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.
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. Sample 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>
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 : __##________________
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>
C
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- define SPACEDIM 20
- define GENERATION 10
- define ALIVE '#'
- define DEAD '_'
/* what happens out of the space: is the world a circle, or
it really ends? */
- define CCOND 0
char space[SPACEDIM]; char tspace[SPACEDIM];
int rrand(int l) {
return (int)((double)l*(double)rand()/((double)RAND_MAX+1.0));
}
void initspace(char *s, int d) {
int i; static const char *tp = "_###_##_#_#_#_#__#__"; for(i=0; (i < strlen(tp)) && (i<d) ; i++) { s[i] = (tp[i] == ALIVE) ? 1 : 0; }
}
void initspace_random(char *s, int d) {
int i; for (i=0; i<d; i++) { s[i] = rrand(2); }
}
/*
count the Number of Alive in the Neighbourhood two kind of "bound condition" can be choosen at compile time
- /
int nalive(const char *s, int i, int d) {
switch ( CCOND ) { case 0: return ((i-1)<0 ? 0 : s[i-1]) + ((i+1)<d ? s[i+1] : 0 ); case 1: return s[ (i+1)%d ] + s[ (i+d-1)%d ]; }
}
void evolve(const char *from, char *to, int d) {
int i; for(i=0; i<d; i++) { if ( from[i] ) { /* 0 neighbour is solitude, 2 are one too much; 1, he's a friend */ if ( nalive(from, i, d) == 1 ) { to[i] = 1; } else { to[i] = 0; } } else { if ( nalive(from, i, d) == 2 ) { /* there must be two, to make a child ... */ to[i] = 1; } else { to[i] = 0; } } }
}
void show(const char *s, int d) {
int i; for(i=0; i<d; i++) { printf("%c", s[i] ? ALIVE : DEAD); } printf("\n");
}
int main()
{
int i; char *from, *to, *t; initspace(space, SPACEDIM); from = space; to = tspace; for(i=0; i<GENERATION; i++) { show(from, SPACEDIM); evolve(from, to, SPACEDIM); t = from; from = to; to = t; } printf("\n"); initspace_random(space, SPACEDIM); from = space; to = tspace; for(i=0; i<GENERATION; i++) { show(from, SPACEDIM); evolve(from, to, SPACEDIM); t = from; from = to; to = t; } return 0;
}</lang>
The output is:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ #_###__#_#_#_#####_# _##_#___#_#_##___##_ _###_____#_###___##_ _#_#______##_#___##_ __#_______###____##_ __________#_#____##_ ___________#_____##_ _________________##_ _________________##_ _________________##_
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:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
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>
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>import std.stdio, std.algorithm;
void main() {
enum ngenerations = 10; enum initial = "0011101101010101001000"; enum table = "00010110";
auto A = new char[initial.length + 2]; A[] = '0'; auto B = A.dup; A[1 .. $-1] = initial;
foreach (_; 0 .. ngenerations) { foreach (i; 1 .. A.length-1) { write(A[i] == '0' ? '_' : '#'); int val = (A[i-1]-'0' << 2) | (A[i]-'0' << 1) | (A[i+1]-'0'); B[i] = table[val]; } swap(A, B); writeln(); }
}</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>
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> <lang>( scratchpad ) "cellular" run _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________</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: __##________________
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>
Some output: <lang haskell>*Life1D> mapM_ print . lahmahgaan $ "_###_##_#_#_#_#__#__" "_###_##_#_#_#_#__#__" "_#_#####_#_#_#______" "__##___##_#_#_______" "__##___###_#________" "__##___#_##_________" "__##____###_________" "__##____#_#_________" "__##_____#__________" "__##________________"
- Life1D> main
"__##_##__#____###__#__#_______#_#_##" "__#####_______#_#______________#_###" "__#___#________#________________##_#" "________________________________###_" "________________________________#_#_" "_________________________________#__" "____________________________________"</lang>
J
<lang j>life1d=: '_#'{~ (2 = 3+/\ 0,],0:)^:a:</lang> Example use: <lang j> life1d ? 20 # 2 _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________</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: __##________________
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".
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>
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> Sample Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 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
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> gives back: <lang Mathematica>###.##.#.#.#.#..#
- .#####.#.#.#....
.##...##.#.#..... .##...###.#...... .##...#.##....... .##....###....... .##....#.#....... .##.....#........ .##.............. .##.............. .##.............. .##.............. .##..............</lang>
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>
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 = ()
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: __##________________
Perl 6
Short though it is, this solution even detects stability. Z+ is a zip metaop with addition, and X== is a cross metaop with equality. (Crossing with a scalar always producing a list of the same length.) We have taken the slight liberty of defining a wraparound universe, but it doesn't matter for this example. <lang perl6>my @c = <_ #>; my @array = '_###_##_#_#_#_#__#__'.comb.map: { $_ eq '#' };
repeat until @array eqv my @prev {
say @c[@prev = @array]; @array = ((@array Z+ @array.rotate(1)) Z+ @array.rotate(-1)) X== 2;
}</lang>
Output:
<lang>_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________</lang>
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:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
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 Swap cG() , nG()
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
<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>
Sample output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
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>
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>
Sample output,
1 _##_____####_#___#_#__ 2 _##_____#__##_____#___ 3 _##________##_________ 4 _##________##_________ 5 _##________##_________ 6 _##________##_________ 7 _##________##_________ 8 _##________##_________ 9 _##________##_________ 10 _##________##_________
Ruby
<lang ruby>def evolve(ary)
new = Array.new(ary.length) new[0] = (ary[0] == 1 and ary[1] == 1) ? 1 : 0 (1..new.length - 2).each {|i| new[i] = ary[i-1] + ary[i] + ary[i+1] == 2 ? 1 : 0} new[-1] = (ary[-2] == 1 and ary[-1] == 1) ? 1 : 0 new
end
def printit(ary)
s = ary.join("") s.gsub!(/1/,"#") s.gsub!(/0/,".") puts s
end
ary = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] printit ary while ary != new=evolve(ary)
printit new ary = new
end</lang>
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................
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: <lang>(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)</lang>
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>