One-dimensional cellular automata
(Redirected from Life in one dimension)
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.
- Related tasks
11l
V gen = ‘_###_##_#_#_#_#__#__’.map(ch -> Int(ch == ‘#’))
L(n) 10
print(gen.map(cell -> (I cell != 0 {‘#’} E ‘_’)).join(‘’))
gen = [0] [+] gen [+] [0]
gen = (0 .< gen.len - 2).map(m -> Int(sum(:gen[m .+ 3]) == 2))- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
8th
\ 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
ACL2
(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)))))
Action!
CHAR FUNC CalcCell(CHAR prev,curr,next)
IF prev='. AND curr='# AND next='# THEN
RETURN ('#)
ELSEIF prev='# AND curr='. AND next='# THEN
RETURN ('#)
ELSEIF prev='# AND curr='# AND next='. THEN
RETURN ('#)
FI
RETURN ('.)
PROC NextGeneration(CHAR ARRAY s)
BYTE i
CHAR prev,curr,next
IF s(0)<4 THEN RETURN FI
prev=s(1) curr=s(2) next=s(3)
i=2
DO
s(i)=CalcCell(prev,curr,next)
i==+1
IF i=s(0) THEN EXIT FI
prev=curr curr=next next=s(i+1)
OD
RETURN
PROC Main()
DEFINE MAXGEN="9"
CHAR ARRAY s=".###.##.#.#.#.#..#.."
BYTE i
FOR i=0 TO MAXGEN
DO
PrintF("Generation %I: %S%E",i,s)
IF i<MAXGEN THEN
NextGeneration(s)
FI
OD
RETURN- Output:
Screenshot from Atari 8-bit computer
Generation 0: .###.##.#.#.#.#..#.. Generation 1: .#.#####.#.#.#...... Generation 2: ..##...##.#.#....... Generation 3: ..##...###.#........ Generation 4: ..##...#.##......... Generation 5: ..##....###......... Generation 6: ..##....#.#......... Generation 7: ..##.....#.......... Generation 8: ..##................ Generation 9: ..##................
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;
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
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- 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
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- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
ALGOL W
Using a string to represent the cells and stopping when the next state is th same as the previous one.
begin
string(20) state;
string(20) nextState;
integer generation;
generation := 0;
state := "_###_##_#_#_#_#__#__";
while begin
write( i_w := 1, s_w := 1, "Generation ", generation, state );
nextState := "____________________";
for cPos := 1 until 18 do begin
string(3) curr;
curr := state( cPos - 1 // 3 );
nextState( cPos // 1 ) := if curr = "_##" or curr = "#_#" or curr = "##_" then "#" else "_"
end for_cPos ;
( state not = nextState )
end do begin
state := nextState;
generation := generation + 1
end while_not_finished
end.- Output:
Generation 0 _###_##_#_#_#_#__#__ Generation 1 _#_#####_#_#_#______ Generation 2 __##___##_#_#_______ Generation 3 __##___###_#________ Generation 4 __##___#_##_________ Generation 5 __##____###_________ Generation 6 __##____#_#_________ Generation 7 __##_____#__________ Generation 8 __##________________
Amazing Hopper
Amazing Hopper flavour "BASICO", in spanish.
VERSION 1:
#include <basico.h>
algoritmo
tamaño de pila 65
x = 0
enlistar (0,0,1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,\
1,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,0,0,\
1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,1,1,0,0) mover a 'x'
x2 = x
decimales '0', token.separador ("")
iterar para ( k=1, #(k<=15), ++k )
imprimir ' #(utf8("Generación #")),k, "\t", x, NL '
iterar para ( j=2, #(j<60), ++j )
#(x2[j] = 0)
cuando ( #( (x[j-1]+x[j]+x[j+1])==2 ) ){
#(x2[j]=1)
}
siguiente
x = x2
siguiente
terminar
- Output:
Generación #1 001110011010110111001111110111011111010011000001010111111100 Generación #2 001010011101111101001000011101110001100011000000101100000100 Generación #3 000100010111000110000000010111010001100011000000011100000000 Generación #4 000000001101000110000000001101100001100011000000010100000000 Generación #5 000000001110000110000000001111100001100011000000001000000000 Generación #6 000000001010000110000000001000100001100011000000000000000000 Generación #7 000000000100000110000000000000000001100011000000000000000000 Generación #8 000000000000000110000000000000000001100011000000000000000000 Generación #9 000000000000000110000000000000000001100011000000000000000000 Generación #10 000000000000000110000000000000000001100011000000000000000000 Generación #11 000000000000000110000000000000000001100011000000000000000000 Generación #12 000000000000000110000000000000000001100011000000000000000000 Generación #13 000000000000000110000000000000000001100011000000000000000000 Generación #14 000000000000000110000000000000000001100011000000000000000000 Generación #15 000000000000000110000000000000000001100011000000000000000000
VERSION 2:
#include <basico.h>
algoritmo
x={}
'0,0,1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0' anidar en lista 'x'
'1,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,0,0' anidar en lista 'x'
'1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,1,1,0,0' anidar en lista 'x'
x2 = x, k=10
decimales '0', token.separador ("")
iterar
imprimir ' #(utf8("Generación #")), #(11-k), "\t", x, NL '
iterar para ( j=2, #(j<60), ++j )
#( x2[j] = ((x[j-1]+x[j]+x[j+1])==2) )
siguiente
x = x2
mientras ' k-- '
terminar
- Output:
Generación #1 001110011010110111001111110111011111010011000001010111111100 Generación #2 001010011101111101001000011101110001100011000000101100000100 Generación #3 000100010111000110000000010111010001100011000000011100000000 Generación #4 000000001101000110000000001101100001100011000000010100000000 Generación #5 000000001110000110000000001111100001100011000000001000000000 Generación #6 000000001010000110000000001000100001100011000000000000000000 Generación #7 000000000100000110000000000000000001100011000000000000000000 Generación #8 000000000000000110000000000000000001100011000000000000000000 Generación #9 000000000000000110000000000000000001100011000000000000000000 Generación #10 000000000000000110000000000000000001100011000000000000000000 Generación #11 000000000000000110000000000000000001100011000000000000000000
Arturo
evolve: function [arr][
ary: [0] ++ arr ++ [0]
ret: new []
loop 1..(size ary)-2 'i [
a: ary\[i-1]
b: ary\[i]
c: ary\[i+1]
if? 2 = a+b+c -> 'ret ++ 1
else -> 'ret ++ 0
]
ret
]
printIt: function [arr][
print replace replace join map arr 'n -> to :string n "0" "_" "1" "#"
]
arr: [0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0]
printIt arr
newGen: evolve arr
while [newGen <> arr][
arr: newGen
newGen: evolve arr
printIt newGen
]
- Output:
_###_##_#_#_#_#__#__ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
AutoHotkey
ahk discussion
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
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
}
}
- Output:
0: . @ @ @ . @ @ . @ . @ . @ . @ . . @ . . 1: . @ . @ @ @ @ @ . @ . @ . @ . . . . . . 2: . . @ @ . . . @ @ . @ . @ . . . . . . . 3: . . @ @ . . . @ @ @ . @ . . . . . . . . 4: . . @ @ . . . @ . @ @ . . . . . . . . . 5: . . @ @ . . . . @ @ @ . . . . . . . . . 6: . . @ @ . . . . @ . @ . . . . . . . . . 7: . . @ @ . . . . . @ . . . . . . . . . . 8: . . @ @ . . . . . . . . . . . . . . . . 9: . . @ @ . . . . . . . . . . . . . . . .
Another new solution (twice size as previous solution) :
cat automata.awk :
#!/usr/local/bin/gawk -f
# User defined functions
function ASCII_to_Binary(str_) {
gsub("_","0",str_); gsub("@","1",str_)
return str_
}
function Binary_to_ASCII(bit_) {
gsub("0","_",bit_); gsub("1","@",bit_)
return bit_
}
function automate(b1,b2,b3) {
a = and(b1,b2,b3)
b = or(b1,b2,b3)
c = xor(b1,b2,b3)
d = a + b + c
return d == 1 ? 1 : 0
}
# For each line in input do
{
str_ = $0
gen = 0
taille = length(str_)
print "0: " str_
do {
gen ? str_previous = str_ : str_previous = ""
gen += 1
str_ = ASCII_to_Binary(str_)
split(str_,tab,"")
str_ = and(tab[1],tab[2])
for (i=1; i<=taille-2; i++) {
str_ = str_ automate(tab[i],tab[i+1],tab[i+2])
}
str_ = str_ and(tab[taille-1],tab[taille])
print gen ": " Binary_to_ASCII(str_)
} while (str_ != str_previous)
}
- Output:
$ echo ".@@@.@@.@.@.@.@..@.." | awk -f automata.awk 0: .@@@.@@.@.@.@.@..@.. 1: _@_@@@@@_@_@_@______ 2: __@@___@@_@_@_______ 3: __@@___@@@_@________ 4: __@@___@_@@_________ 5: __@@____@@@_________ 6: __@@____@_@_________ 7: __@@_____@__________ 8: __@@________________ 9: __@@________________
BASIC
Applesoft BASIC
100 HOME
110 n = 10
120 READ w : DIM x(w+1),x2(w+1) : FOR i = 1 TO w : READ x(i) : NEXT
130 FOR k = 1 TO n
140 FOR j = 1 TO w
150 IF x(j) THEN PRINT "#";
155 IF NOT x(j) THEN PRINT "_";
160 IF x(j-1)+x(j)+x(j+1) = 2 THEN x2(j) = 1
165 IF x(j-1)+x(j)+x(j+1) <> 2 THEN x2(j) = 0
170 NEXT : PRINT
180 FOR j = 1 TO w : x(j) = x2(j) : NEXT
190 NEXT
200 DATA 20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0
BASIC256
arraybase 1
dim start = {0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0}
dim sgtes(start[?]+1)
for k = 0 to 9
print "Generation "; k; ": ";
for j = 0 to start[?]-1
if start[j] then print "#"; else print "_";
if start[j-1] + start[j] + start[j+1] = 2 then sgtes[j] = 1 else sgtes[j] = 0
next j
print
for j = 0 to start[?]-1
start[j] = sgtes[j]
next j
next kBBC BASIC
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%
- 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
Chipmunk Basic
100 CLS
110 LET n = 10
120 READ w
121 DIM x(w+1): DIM x2(w+1)
122 FOR i = 1 TO w : READ x(i) : NEXT i
130 FOR k = 1 TO n
140 FOR j = 1 TO w
150 IF x(j) THEN PRINT "#"; ELSE PRINT "_";
160 IF x(j-1)+x(j)+x(j+1) = 2 THEN LET x2(j) = 1 ELSE LET x2(j) = 0
170 NEXT j
171 PRINT
180 FOR j = 1 TO w : LET x(j) = x2(j) : NEXT j
190 NEXT k
200 DATA 20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0
210 END
FreeBASIC
#define SIZE 640
randomize timer
dim as ubyte arr(0 to SIZE-1, 0 to 1)
dim as uinteger i
for i = 0 to SIZE - 1 'initialise array with zeroes and ones
arr(i, 0)=int(rnd+0.5)
next i
screen 12 'display graphically
dim as string ch=" "
dim as uinteger j = 0, cur = 0, nxt, prv, neigh
while not ch = "q" or ch = "Q"
for i = 0 to SIZE - 1
pset(i, j), 8+7*arr(i,cur) 'print off cells as grey, on cells as bright white
nxt = (i + 1) mod SIZE
prv = (i - 1)
if prv < 0 then prv = SIZE - 1 'let's have a wrap-around array for fun
neigh = arr(prv, cur) + arr(nxt, cur)
if arr(i, cur) = 0 then 'evolution rules
if neigh = 2 then
arr(i, 1-cur) = 1
else
arr(i, 1-cur) = 0
end if
else
if neigh = 0 or neigh = 2 then
arr(i, 1-cur) = 0
else
arr(i, 1-cur) = 1
end if
end if
next i
j = j + 1
cur = 1 - cur
do
ch = inkey
if ch <> "" then exit do 'press any key to advance the sim
'or Q to exit
loop
wend
GFA Basic
'
' 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$,i%,1)="1"
world!(i%,0)=TRUE
ENDIF
NEXT i%
' set references to cur and new
cur%=0
new%=1
RETURN
'
' Display the world
'
PROCEDURE display_world
LOCAL i%
FOR i%=1 TO size%
IF world!(i%,cur%)
PRINT "#";
ELSE
PRINT ".";
ENDIF
NEXT i%
PRINT ""
RETURN
'
' Create new version of world
'
PROCEDURE update_world
LOCAL i%
FOR i%=1 TO size%
world!(i%,new%)=@new_state(@get_value(i%))
NEXT i%
' reverse cur/new
cur%=1-cur%
new%=1-new%
RETURN
'
' Test if cur/new states are the same
'
FUNCTION same_state
LOCAL i%
FOR i%=1 TO size%
IF world!(i%,cur%)<>world!(i%,new%)
RETURN FALSE
ENDIF
NEXT i%
RETURN TRUE
ENDFUNC
'
' Return new state of cell given value
'
FUNCTION new_state(value%)
SELECT value%
CASE 0,1,2,4,7
RETURN FALSE
CASE 3,5,6
RETURN TRUE
ENDSELECT
ENDFUNC
'
' Compute value for cell + neighbours
'
FUNCTION get_value(cell%)
LOCAL result%
result%=0
IF world!(cell%-1,cur%)
result%=result%+4
ENDIF
IF world!(cell%,cur%)
result%=result%+2
ENDIF
IF world!(cell%+1,cur%)
result%=result%+1
ENDIF
RETURN result%
ENDFUNC
GW-BASIC
The Chipmunk Basic solution works without any changes.
Liberty BASIC
' [RC] 'One-dimensional cellular automata'
' does not wrap so fails for some rules
rule$ ="00010110" ' Rule 22 decimal
state$ ="0011101101010101001000"
for j =1 to 20
print state$
oldState$ =state$
state$ ="0"
for k =2 to len( oldState$) -1
NHood$ =mid$( oldState$, k -1, 3) ' pick 3 char neighbourhood and turn binary string to decimal
vNHood =0
for kk =3 to 1 step -1
vNHood =vNHood +val( mid$( NHood$, kk, 1)) *2^( 3 -kk)
next kk
' .... & use it to index into rule$ to find appropriate new value
state$ =state$ +mid$( rule$, vNHood +1, 1)
next k
state$ =state$ +"0"
next j
endLocomotive Basic
10 MODE 1:n=10:READ w:DIM x(w+1),x2(w+1):FOR i=1 to w:READ x(i):NEXT
20 FOR k=1 TO n
30 FOR j=1 TO w
40 IF x(j) THEN PRINT "#"; ELSE PRINT "_";
50 IF x(j-1)+x(j)+x(j+1)=2 THEN x2(j)=1 ELSE x2(j)=0
60 NEXT:PRINT
70 FOR j=1 TO w:x(j)=x2(j):NEXT
80 NEXT
90 DATA 20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0
- Output:
MSX Basic
The Chipmunk Basic solution works without any changes.
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() <> ""
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
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
- Output:
Generation 0 : _###_##_#_#_#_#__#__ Generation 1 : _#_#####_#_#_#______ Generation 2 : __##___##_#_#_______ Generation 3 : __##___###_#________ Generation 4 : __##___#_##_________ Generation 5 : __##____###_________ Generation 6 : __##____#_#_________ Generation 7 : __##_____#__________ Generation 8 : __##________________ Generation 9 : __##________________
Quite BASIC
The Chipmunk Basic solution works without any changes.
Run BASIC
The Liberty BASIC solution works without any changes.
Sinclair ZX81 BASIC
Works with the unexpanded (1k RAM) ZX81.
10 LET N$="01110110101010100100"
20 LET G=1
30 PRINT N$
40 LET O$=N$
50 LET N$=""
60 PRINT AT 0,28;G
70 LET N=0
80 FOR I=1 TO LEN O$
90 IF I=1 THEN GOTO 120
100 LET N=VAL O$(I-1)
110 IF I=LEN O$ THEN GOTO 130
120 LET N=N+VAL O$(I+1)
130 IF N=0 THEN LET N$=N$+"0"
140 IF N=1 THEN LET N$=N$+O$(I)
150 IF N=2 THEN LET N$=N$+STR$ NOT VAL O$(I)
160 PRINT AT 0,I-1;N$(I)
170 NEXT I
180 LET G=G+1
190 IF N$<>O$ THEN GOTO 40
- Output:
The program overwrites each cell on the screen as it updates it (which it does quite slowly—there is no difficulty about watching what it is doing), with a counter to the right showing the generation it is currently working on. When it is part of the way through, for example, the display looks like this:
00110001011000000000 5
It halts when a stable state has been reached:
00110000000000000000 9
Visual Basic .NET
This implementation is run from the command line. The command is followed by a string of either 1's or #'s for an active cell, or 0's or _'s for an inactive one.
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 ModuleOutput:
C:\>CellularAutomata _###_##_#_#_#_#__#__ 000: _###_##_#_#_#_#__#__ 001: _#_#####_#_#_#______ 002: __##___##_#_#_______ 003: __##___###_#________ 004: __##___#_##_________ 005: __##____###_________ 006: __##____#_#_________ 007: __##_____#__________ 008: __##________________ Sample stable after 8 generations.
Yabasic
10 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 "_"; END IF
50 IF x(j-1)+x(j)+x(j+1)=2 THEN x2(j)=1 ELSE x2(j)=0 END IF
60 NEXT:PRINT
70 FOR j=1 TO w:x(j)=x2(j):NEXT
80 NEXT
90 DATA 20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0Other solution
start$ = "0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0"
dim x$(1)
for k = 1 to 10
n = token(start$, x$(), ",")
redim x$(n+1)
start$ = ""
for j = 1 to n
if val(x$(j)) then print "#"; else print "_"; end if
test = abs(val(x$(j-1)) + val(x$(j)) + val(x$(j+1)) = 2)
start$ = start$ + str$(test) + ","
next j
print
next kBatch File
This implementation will not stop showing generations, unless the cellular automata is already stable.
@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
- Output:
| __###__##_#_##_###__######_###_#####_#__##_____#_#_#######__ |
| __#_#__###_#####_#__#____###_###___##___##______#_##_____#__ |
| ___#___#_###___##________#_###_#___##___##_______###________ |
| ________##_#___##_________##_##____##___##_______#_#________ |
| ________###____##_________#####____##___##________#_________ |
| ________#_#____##_________#___#____##___##__________________ |
| _________#_____##__________________##___##__________________ |
| _______________##__________________##___##__________________ |
...The sample is now stable.
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 > >$"!"> 20g10g1+p 20g1+:20p
^ v_10p10g
> ^
Bracmat
( ( evolve
= n z
. @( !arg
: %?n ? @?z
: ?
( ( ( 000
| 001
| 010
| 100
| 111
)
& 0 !n:?n
| (011|101|110)
& 1 !n:?n
)
& ~`
)
?
)
| rev$(str$(!z !n))
)
& 11101101010101001001:?S
& :?seen
& whl
' ( ~(!seen:? !S ?)
& out$!S
& !S !seen:?seen
& evolve$!S:?S
)
);- Output:
11101101010101001001 10111110101010000001 11100011010100000001 10100011101000000001 11000010110000000001 11000001110000000001 11000001010000000001 11000000100000000001 11000000000000000001
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;
}
- Output:
###_##_#_#_#_#__#__ #_#####_#_#_#______ _##___##_#_#_______ _##___###_#________ _##___#_##_________ _##____###_________ _##____#_#_________ _##_____#__________ _##________________
Similar to above, but without a backup string:
#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;
}
This version uses the rule where a cell is alive in the next generation if the sum of itself and its neighbors is exactly 2.
#include <stdio.h>
#include <string.h>
#define SIZE 21
void print_gen(int gen[], int size) {
for (int i = 0; i < size; i++) {
printf("%c", gen[i] ? '#' : '_');
}
printf("\n");
}
void evolve(int gen[], int size) {
int next_gen[size + 2];
next_gen[0] = next_gen[size + 1] = 0;
for (int i = 0; i < size; i++) {
next_gen[i + 1] = gen[i];
}
for (int i = 0; i < size; i++) {
gen[i] = (next_gen[i] + next_gen[i + 1] + next_gen[i + 2]) == 2;
}
}
int main() {
char initial[] = "_###_##_#_#_#_#__#__";
int gen[SIZE];
for (int i = 0; i < SIZE; i++) {
gen[i] = initial[i] == '#';
}
for (int n = 0; n < 10; n++) {
print_gen(gen, SIZE);
evolve(gen, SIZE);
}
return 0;
}
- Output:
_###_##_#_#_#_#__#___ _#_#####_#_#_#_______ __##___##_#_#________ __##___###_#_________ __##___#_##__________ __##____###__________ __##____#_#__________ __##_____#___________ __##_________________ __##_________________
C#
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("");
}
}
}
}
C++
Uses std::bitset for efficient packing of bit values.
#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;
}
}
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
Ceylon
shared abstract class Cell(character) of alive | dead {
shared Character character;
string => character.string;
shared formal Cell opposite;
}
shared object alive extends Cell('#') {
opposite => dead;
}
shared object dead extends Cell('_') {
opposite => alive;
}
shared Map<Character, Cell> cellsByCharacter = map { for (cell in `Cell`.caseValues) cell.character->cell };
shared class Automata1D({Cell*} initialCells) {
value permanentFirstCell = initialCells.first else dead;
value permanentLastCell = initialCells.last else dead;
value cells = Array { *initialCells.rest.exceptLast };
shared Boolean evolve() {
value newCells = Array {
for (index->cell in cells.indexed)
let (left = cells[index - 1] else permanentFirstCell,
right = cells[index + 1] else permanentLastCell,
neighbours = [left, right],
bothAlive = neighbours.every(alive.equals),
bothDead = neighbours.every(dead.equals))
if (bothAlive)
then cell.opposite
else if (cell == alive && bothDead)
then dead
else cell
};
if (newCells == cells) {
return false;
}
newCells.copyTo(cells);
return true;
}
string => permanentFirstCell.string + "".join(cells) + permanentLastCell.string;
}
shared Automata1D? automata1d(String string) =>
let (cells = string.map((Character element) => cellsByCharacter[element]))
if (cells.every((Cell? element) => element exists))
then Automata1D(cells.coalesced)
else null;
shared void run() {
assert (exists automata = automata1d("__###__##_#_##_###__######_###_#####_#__##_____#_#_#######__"));
variable value generation = 0;
print("generation ``generation`` ``automata``");
while (automata.evolve() && generation<10) {
print("generation `` ++generation `` ``automata``");
}
}
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)))))
one-dimensional-cellular-automata> (doseq [cells (generate 9 "_###_##_#_#_#_#__#__")]
(println cells))
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
nil
Another way:
#!/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)))))
Yet another way, easier to understand
(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))
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
.
- Output:
0: .@@@.@@.@.@.@.@..@.. 1: .@.@@@@@.@.@.@...... 2: ..@@...@@.@.@....... 3: ..@@...@@@.@........ 4: ..@@...@.@@......... 5: ..@@....@@@......... 6: ..@@....@.@......... 7: ..@@.....@.......... 8: ..@@................ 9: ..@@................
=pre>###_##_#_#_#_#__#__
- _#####_#_#_#______
_##___##_#_#_______ _##___###_#________ _##___#_##_________ _##____###_________ _##____#_#_________ _##_____#__________ _##________________=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 ".###.##.#.#.#.#..#..")
- Output:
> coffee cellular_automata.coffee .###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ equilibrium achieved
Common Lisp
Based upon the Ruby version.
(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))
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))
.###.##.#.#.#.#..#..
.#.#####.#.#.#......
..##...##.#.#.......
..##...###.#........
..##...#.##.........
..##....###.........
..##....#.#.........
..##.....#..........
..##................
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;
}
}
- Output:
__###_##_#_#_#_#__#___ __#_#####_#_#_#_______ ___##___##_#_#________ ___##___###_#_________ ___##___#_##__________ ___##____###__________ ___##____#_#__________ ___##_____#___________ ___##_________________ ___##_________________
Alternative Version
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);
}
- 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.
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);
}
}
The output is the same as the second version.
DWScript
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;
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
Déjà Vu
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- Output:
001110011010110111001111110111011111010011000001010111111100 001010011101111101001000011101110001100011000000101100000100 000100010111000110000000010111010001100011000000011100000000 000000001101000110000000001101100001100011000000010100000000 000000001110000110000000001111100001100011000000001000000000 000000001010000110000000001000100001100011000000000000000000 000000000100000110000000000000000001100011000000000000000000 000000000000000110000000000000000001100011000000000000000000 000000000000000110000000000000000001100011000000000000000000
Delphi
type TGame = string[20];
type TPattern = string[3];
function GetSubPattern(Game: TGame; Inx: integer): TPattern;
{Get the pattern of three cells adjacent to Inx}
var I: integer;
begin
Result:='';
{Cells off the ends of the array are consider empty}
for I:=Inx-1 to Inx+1 do
if (I<1) or (I>Length(Game)) then Result:=Result+' '
else Result:=Result+Game[I];
end;
function GetNewValue(P: TPattern): char;
{Calculate the new value for a cell based}
{the pattern of neighboring cells}
begin
if P=' ' then Result:=' ' { No change}
else if P=' #' then Result:=' ' { No change}
else if P=' # ' then Result:=' ' { Dies without enough neighbours}
else if P=' ##' then Result:='#' { Needs one neighbour to survive}
else if P='# ' then Result:=' ' { No change}
else if P='# #' then Result:='#' { Two neighbours giving birth}
else if P='## ' then Result:='#' { Needs one neighbour to survive}
else if P='###' then Result:=' '; { Starved to death.}
end;
procedure CellularlAutoGame(Memo: TMemo);
{Iterate through steps of evolution of cellular automaton}
var GameArray,NextArray: TGame;
var P: string [3];
var I,G: integer;
begin
{Start arrangement}
GameArray:=' ### ## # # # # # ';
for G:=1 to 10 do
begin
{Display current game situation}
Memo.Lines.Add(GameArray);
{Evolve each cell in the array}
for I:=1 to Length(GameArray) do
begin
P:=GetSubPattern(GameArray,I);
NextArray[I]:=GetNewValue(P);
end;
GameArray:=NextArray;
end;
end;
- Output:
### ## # # # # # # ##### # # # ## ## # # ## ### # ## # ## ## ### ## # # ## # ## ## Elapsed Time: 9.784 ms.
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
}def rosettaRule := [
" " => " ",
" #" => " ",
" # " => " ",
" ##" => "#",
"# " => " ",
"# #" => "#",
"## " => "#",
"###" => " ",
].get
? play(" ### ## # # # # # ", rosettaRule, 9, stdout)
0 | ### ## # # # # #
1 | # ##### # # #
2 | ## ## # #
3 | ## ### #
4 | ## # ##
5 | ## ###
6 | ## # #
7 | ## #
8 | ##
9 | ##
# value: " ## "EasyLang
map[] = [ 0 0 0 1 0 1 1 0 ]
cell[] = [ 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 ]
len celln[] len cell[]
proc evolve . .
for i = 2 to len cell[] - 1
ind = cell[i - 1] + 2 * cell[i] + 4 * cell[i + 1] + 1
celln[i] = map[ind]
.
swap celln[] cell[]
.
proc show . .
for v in cell[]
if v = 1
write "#"
else
write "."
.
.
print ""
.
show
for i to 9
evolve
show
.- Output:
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ ..##................
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
- Output:
1011101110 0110111010 0111101100 0100111100 0000100100 0000000000 0000000000 0000000000 0000000000 0000000000
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])
- Output:
Generation 0: .###.##.#.#.#.#..#.. Generation 1: .#.#####.#.#.#...... Generation 2: ..##...##.#.#....... Generation 3: ..##...###.#........ Generation 4: ..##...#.##......... Generation 5: ..##....###......... Generation 6: ..##....#.#......... Generation 7: ..##.....#.......... Generation 8: ..##................ Generation 9: ..##................
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
}
Link to live demo: https://dc25.github.io/oneDimensionalCellularAutomataElm/
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]).
Example execution:
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: ___##_________________
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- 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
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)- Output:
Generation 0: ####__#_###_#_#_#_#_##___##_##__ Generation 1: ___#___##_##_#_#_#_###___#####__ Generation 2: _______######_#_#_##_#___#___#__ Generation 3: _______#____##_#_####___________ Generation 4: ____________###_##__#___________ Generation 5: ____________#_####______________ Generation 6: _____________##__#______________ Generation 7: _____________##_________________ Generation 8: _____________##_________________
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
( scratchpad ) "cellular" run _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
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)
}
}
}FOCAL
1.1 S OLD(2)=1; S OLD(3)=1; S OLD(4)=1; S OLD(6)=1; S OLD(7)=1
1.2 S OLD(9)=1; S OLD(11)=1; S OLD(13)=1; S OLD(15)=1; S OLD(18)=1
1.3 F N=1,10; D 2
1.4 Q
2.1 F X=1,20; D 3
2.2 F X=1,20; D 6
2.3 F X=1,20; S OLD(X)=NEW(X)
2.4 T !
3.1 I (OLD(X-1)+OLD(X)+OLD(X+1)-2)4.1,5.1,4.1
4.1 S NEW(X)=0
5.1 S NEW(X)=1
6.1 I (-OLD(X))7.1,8.1,8.1
7.1 T "#"
8.1 T "."- Output:
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ ..##................
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
ouput
### ## # # # # #
# ##### # # #
## ## # #
## ### #
## # ##
## ###
## # #
## #
##
## ok
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
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Go
Sequential
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]
}
}
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
Concurrent
Computations run on each cell concurrently. Separate read and write phases. Single array of cells.
package main
import (
"fmt"
"sync"
)
const (
start = "_###_##_#_#_#_#__#__"
offLeft = '_'
offRight = '_'
dead = '_'
)
func main() {
fmt.Println(start)
a := make([]byte, len(start)+2)
a[0] = offLeft
copy(a[1:], start)
a[len(a)-1] = offRight
var read, write sync.WaitGroup
read.Add(len(start) + 1)
for i := 1; i <= len(start); i++ {
go cell(a[i-1:i+2], &read, &write)
}
for i := 0; i < 10; i++ {
write.Add(len(start) + 1)
read.Done()
read.Wait()
read.Add(len(start) + 1)
write.Done()
write.Wait()
fmt.Println(string(a[1 : len(a)-1]))
}
}
func cell(kernel []byte, read, write *sync.WaitGroup) {
var next byte
for {
l, v, r := kernel[0], kernel[1], kernel[2]
read.Done()
switch {
case l != r:
next = v
case v == dead:
next = l
default:
next = dead
}
read.Wait()
kernel[1] = next
write.Done()
write.Wait()
}
}
Output is same as sequential version.
Groovy
Solution:
def life1D = { self ->
def right = self[1..-1] + [false]
def left = [false] + self[0..-2]
[left, self, right].transpose().collect { hood -> hood.count { it } == 2 }
}
Test:
def cells = ('_###_##_#_#_#_#__#__' as List).collect { it == '#' }
println "Generation 0: ${cells.collect { g -> g ? '#' : '_' }.join()}"
(1..9).each {
cells = life1D(cells)
println "Generation ${it}: ${cells.collect { g -> g ? '#' : '_' }.join()}"
}
- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Haskell
import Data.List (unfoldr)
import System.Random (newStdGen, randomRs)
bnd :: String -> Char
bnd "_##" = '#'
bnd "#_#" = '#'
bnd "##_" = '#'
bnd _ = '_'
nxt :: String -> String
nxt = unfoldr go . ('_' :) . (<> "_")
where
go [_, _] = Nothing
go xs = Just (bnd $ take 3 xs, drop 1 xs)
lahmahgaan :: String -> [String]
lahmahgaan xs =
init
. until
((==) . last <*> last . init)
((<>) <*> pure . nxt . last)
$ [xs, nxt xs]
main :: IO ()
main =
newStdGen
>>= ( mapM_ putStrLn . lahmahgaan
. map ("_#" !!)
. take 36
. randomRs (0, 1)
)
- Output:
For example:
_##_#_#__#_#_#_#_###_#######_#_#__## _###_#____#_#_#_##_###_____##_#___## _#_##______#_#_#####_#_____###____## __###_______#_##___##______#_#____## __#_#________###___##_______#_____## ___#_________#_#___##_____________## ______________#____##_____________## ___________________##_____________##
Icon and Unicon
An alternative approach is to represent the automaton as a string. The following solution takes advantage of the implicit type coercions between string and numeric values in Icon and Unicon. It also surrounds the automaton with a border of 'dead' (always 0) cells to eliminate the need to special case the first and last cells in the automaton. Although the main procedure displays up to the first 10 generations, the evolve procedure fails if a new generation is unchanged from the previous, stopping the generation cycle early.
procedure main(A)
A := if *A = 0 then ["01110110101010100100"]
CA := show("0"||A[1]||"0") # add always dead border cells
every CA := show(|evolve(CA)\10) # limit to max of 10 generations
end
procedure show(ca)
write(ca[2:-1]) # omit border cells
return ca
end
procedure evolve(CA)
newCA := repl("0",*CA)
every newCA[i := 2 to (*CA-1)] := (CA[i-1]+CA[i]+CA[i+1] = 2, "1")
return CA ~== newCA # fail if no change
end
- A couple of sample runs:
->odca 01110110101010100100 01011111010101000000 00110001101010000000 00110001110100000000 00110001011000000000 00110000111000000000 00110000101000000000 00110000010000000000 00110000000000000000 ->odca 01110110 01110110 01011110 00110010 00110000 ->
Insitux
(function next cells
(... str
(map (comp str (count ["#"]) (= 2) #(% "#" "_"))
(str "_" cells)
cells
(str (skip 1 cells) "_"))))
(function generate n cells
(join "\n" (reductions next cells (range n))))- Output:
Invoking (generate 9 "_###_##_#_#_#_#__#__")
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
J
life1d=: '_#'{~ (2 = 3+/\ 0,],0:)^:a:
- Example use:
life1d ? 20 # 2
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
Alternative implementation:
Rule=:2 :0 NB. , m: number of generations, n: rule number
'_#'{~ (3 ((|.n#:~8#2) {~ #.)\ 0,],0:)^:(i.m)
)
- Example use:
9 Rule 104 '#'='_###_##_#_#_#_#__#__'
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
Java
This example requires a starting generation of at least length two (which is what you need for anything interesting anyway).
public class Life{
public static void main(String[] args) throws Exception{
String start= "_###_##_#_#_#_#__#__";
int numGens = 10;
for(int i= 0; i < numGens; i++){
System.out.println("Generation " + i + ": " + start);
start= life(start);
}
}
public static String life(String lastGen){
String newGen= "";
for(int i= 0; i < lastGen.length(); i++){
int neighbors= 0;
if (i == 0){//left edge
neighbors= lastGen.charAt(1) == '#' ? 1 : 0;
} else if (i == lastGen.length() - 1){//right edge
neighbors= lastGen.charAt(i - 1) == '#' ? 1 : 0;
} else{//middle
neighbors= getNeighbors(lastGen.substring(i - 1, i + 2));
}
if (neighbors == 0){//dies or stays dead with no neighbors
newGen+= "_";
}
if (neighbors == 1){//stays with one neighbor
newGen+= lastGen.charAt(i);
}
if (neighbors == 2){//flips with two neighbors
newGen+= lastGen.charAt(i) == '#' ? "_" : "#";
}
}
return newGen;
}
public static int getNeighbors(String group){
int ans= 0;
if (group.charAt(0) == '#') ans++;
if (group.charAt(2) == '#') ans++;
return ans;
}
}
- 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.
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));
}
}
- 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.
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;
}
- Example usage:
alert(caStep([0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]));
shows an alert with "0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0".
jq
The main point of interest in the following is perhaps the way the built-in function "recurse" is used to continue the simulation until quiescence.
# The 1-d cellular automaton:
def next:
# Conveniently, jq treats null as 0 when it comes to addition
# so there is no need to fiddle with the boundaries
. as $old
| reduce range(0; length) as $i
([];
($old[$i-1] + $old[$i+1]) as $s
| if $s == 0 then .[$i] = 0
elif $s == 1 then .[$i] = (if $old[$i] == 1 then 1 else 0 end)
else .[$i] = (if $old[$i] == 1 then 0 else 1 end)
end);
# pretty-print an array:
def pp: reduce .[] as $i (""; . + (if $i == 0 then " " else "*" end));
# continue until quiescence:
def go: recurse(. as $prev | next | if . == $prev then empty else . end) | pp;
# Example:
[0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] | go- Output:
$ jq -c -r -n -f One-dimensional_cellular_automata.jq
*** ** * * * * *
* ***** * * *
** ** * *
** *** *
** * **
** ***
** * *
** *
**
Julia
Julia: Implementation as a function accepting a Vector of Bool
automaton(g::Vector{Bool}) =
for i ∈ 0:9
println(join(alive ? '#' : '_' for alive ∈ g))
g = ([false; g[1:end-1]] .+ g .+ [g[2:end]; false]) .== 2
end
automaton([c == '#' for c ∈ "_###_##_#_#_#_#__#__"])
Julia: Implementation as an iterable struct
struct Automaton g₀::Vector{Bool} end
Base.iterate(a::Automaton, g = a.g₀) =
g, ([false; g[1:end-1]] .+ g .+ [g[2:end]; false]) .== 2
Base.show(io::IO, a::Automaton) = for g in Iterators.take(a, 10)
println(io, join(alive ? '#' : '_' for alive ∈ g)) end
Automaton([c == '#' for c ∈ "_###_##_#_#_#_#__#__"])
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
K
f:{2=+/(0,x,0)@(!#x)+/:!3}
- Example usage:
`0:"_X"@f\0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0
_XXX_XX_X_X_X_X__X__
_X_XXXXX_X_X_X______
__XX___XX_X_X_______
__XX___XXX_X________
__XX___X_XX_________
__XX____XXX_________
__XX____X_X_________
__XX_____X__________
__XX________________
Kotlin
// version 1.1.4-3
val trans = "___#_##_"
fun v(cell: StringBuilder, i: Int) = if (cell[i] != '_') 1 else 0
fun evolve(cell: StringBuilder, backup: StringBuilder): Boolean {
val len = cell.length - 2
var diff = 0
for (i in 1 until len) {
/* use left, self, right as binary number bits for table index */
backup[i] = trans[v(cell, i - 1) * 4 + v(cell, i) * 2 + v(cell, i + 1)]
diff += if (backup[i] != cell[i]) 1 else 0
}
cell.setLength(0)
cell.append(backup)
return diff != 0
}
fun main(args: Array<String>) {
val c = StringBuilder("_###_##_#_#_#_#__#__")
val b = StringBuilder("____________________")
do {
println(c.substring(1))
}
while (evolve(c,b))
}
- Output:
###_##_#_#_#_#__#__ #_#####_#_#_#______ _##___##_#_#_______ _##___###_#________ _##___#_##_________ _##____###_________ _##____#_#_________ _##_____#__________ _##________________
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- Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Lua
num_iterations = 9
f = { 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0 }
function Output( f, l )
io.write( l, ": " )
for i = 1, #f do
local c
if f[i] == 1 then c = '#' else c = '_' end
io.write( c )
end
print ""
end
Output( f, 0 )
for l = 1, num_iterations do
local g = {}
for i = 2, #f-1 do
if f[i-1] + f[i+1] == 1 then
g[i] = f[i]
elseif f[i] == 0 and f[i-1] + f[i+1] == 2 then
g[i] = 1
else
g[i] = 0
end
end
if f[1] == 1 and f[2] == 1 then g[1] = 1 else g[1] = 0 end
if f[#f] == 1 and f[#f-1] == 1 then g[#f] = 1 else g[#f] = 0 end
f, g = g, f
Output( f, l )
end
- Output:
0: _###_##_#_#_#_#__#__ 1: _#_#####_#_#_#______ 2: __##___##_#_#_______ 3: __##___###_#________ 4: __##___#_##_________ 5: __##____###_________ 6: __##____#_#_________ 7: __##_____#__________ 8: __##________________ 9: __##________________
M4
divert(-1)
define(`set',`define(`$1[$2]',`$3')')
define(`get',`defn(`$1[$2]')')
define(`setrange',`ifelse(`$3',`',$2,`define($1[$2],$3)`'setrange($1,
incr($2),shift(shift(shift($@))))')')
dnl throw in sentinels at each end (0 and size+1) to make counting easy
define(`new',`set($1,size,eval($#-1))`'setrange($1,1,
shift($@))`'set($1,0,0)`'set($1,$#,0)')
define(`for',
`ifelse($#,0,``$0'',
`ifelse(eval($2<=$3),1,
`pushdef(`$1',$2)$4`'popdef(`$1')$0(`$1',incr($2),$3,`$4')')')')
define(`show',
`for(`k',1,get($1,size),`get($1,k) ')')
dnl swap(`a',a,`b') using arg stack for temp
define(`swap',`define(`$1',$3)`'define(`$3',$2)')
define(`nalive',
`eval(get($1,decr($2))+get($1,incr($2)))')
setrange(`live',0,0,1,0)
setrange(`dead',0,0,0,1)
define(`nv',
`ifelse(get($1,z),0,`get(dead,$3)',`get(live,$3)')')
define(`evolve',
`for(`z',1,get($1,size),
`set($2,z,nv($1,z,nalive($1,z)))')')
new(`a',0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0)
set(`b',size,get(`a',size))`'set(`b',0,0)`'set(`b',incr(get(`a',size)),0)
define(`x',`a')
define(`y',`b')
divert
for(`j',1,10,
`show(x)`'evolve(`x',`y')`'swap(`x',x,`y')
')`'show(x)- 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:
CellularAutomaton[{{0,0,_}->0,{0,1,0}->0,{0,1,1}->1,{1,0,0}->0,{1,0,1}->1,{1,1,0}->1,{1,1,1}->0},{{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1},0},12]
Print @@@ (% /. {1 -> "#", 0 -> "."});
For succinctness, an integral rule can be used:
CellularAutomaton[2^^01101000 (* == 104 *), {{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1}, 0}, 12];
- Output:
###.##.#.#.#.#..#
#.#####.#.#.#....
.##...##.#.#.....
.##...###.#......
.##...#.##.......
.##....###.......
.##....#.#.......
.##.....#........
.##..............
.##..............
.##..............
.##..............
.##..............
MATLAB / Octave
function one_dim_cell_automata(v,n)
V='_#';
while n>=0;
disp(V(v+1));
n = n-1;
v = filter([1,1,1],1,[0,v,0]);
v = v(3:end)==2;
end;
end
- 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.
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.
- Output:
Generation 0 _###_##_#_#_#_#__#__ Generation 1 _#_#####_#_#_#______ Generation 2 __##___##_#_#_______ Generation 3 __##___###_#________ Generation 4 __##___#_##_________ Generation 5 __##____###_________ Generation 6 __##____#_#_________ Generation 7 __##_____#__________ Generation 8 __##________________ Generation 9 __##________________
MontiLang
30 VAR length .
35 VAR height .
FOR length 0 ENDFOR 1 0 ARR VAR list .
length 1 - VAR topLen .
FOR topLen 0 ENDFOR 1 ARR VAR topLst .
DEF getNeighbors
1 - VAR tempIndex .
GET tempIndex SWAP
tempIndex 1 + VAR tempIndex .
GET tempIndex SWAP
tempIndex 1 + VAR tempIndex .
GET tempIndex SWAP .
FOR 3 TOSTR ROT ENDFOR
FOR 2 SWAP + ENDFOR
ENDDEF
DEF printArr
LEN 1 - VAR stLen .
0 VAR j .
FOR stLen
GET j
TOSTR OUT .
j 1 + VAR j .
ENDFOR
|| PRINT .
ENDDEF
FOR height
FOR length 0 ENDFOR ARR VAR next .
1 VAR i .
FOR length
list i getNeighbors VAR last .
i 1 - VAR ind .
last |111| ==
IF : .
next 0 INSERT ind
ENDIF
last |110| ==
IF : .
next 1 INSERT ind
ENDIF
last |101| ==
IF : .
next 1 INSERT ind
ENDIF
last |100| ==
IF : .
next 0 INSERT ind
ENDIF
last |011| ==
IF : .
next 1 INSERT ind
ENDIF
last |010| ==
IF : .
next 1 INSERT ind
ENDIF
last |001| ==
IF : .
next 1 INSERT ind
ENDIF
last |000| ==
IF : .
next 0 INSERT ind
ENDIF
clear
i 1 + VAR i .
ENDFOR
next printArr .
next 0 ADD APPEND . VAR list .
ENDFORNial
(life.nial)
% we need a way to write a values and pass the same back
wi is rest link [write, pass]
% calculate the neighbors by rotating the array left and right and joining them
neighbors is pack [pass, sum [-1 rotate, 1 rotate]]
% calculate the individual birth and death of a single array element
igen is fork [ = [ + [first, second], 3 first], 0 first, = [ + [first, second], 2 first], 1 first, 0 first ]
% apply that to the array
nextgen is each igen neighbors
% 42
life is fork [ > [sum pass, 0 first], life nextgen wi, pass ]- Using it:
|loaddefs 'life.nial'
|I := [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
|life INim
import random
type
BoolArray = array[30, bool]
Symbols = array[bool, char]
proc neighbours(map: BoolArray, i: int): int =
if i > 0: inc(result, int(map[i - 1]))
if i + 1 < len(map): inc(result, int(map[i + 1]))
proc print(map: BoolArray, symbols: Symbols) =
for i in map: write(stdout, symbols[i])
write(stdout, "\l")
proc randomMap: BoolArray =
randomize()
for i in mitems(result): i = sample([true, false])
const
num_turns = 20
symbols = ['_', '#']
T = true
F = false
var map =
[F, T, T, T, F, T, T, F, T, F, T, F, T, F, T,
F, F, T, F, F, F, F, F, F, F, F, F, F, F, F]
# map = randomMap() # uncomment for random start
print(map, symbols)
for _ in 0 ..< num_turns:
var map2 = map
for i, v in pairs(map):
map2[i] =
if v: neighbours(map, i) == 1
else: neighbours(map, i) == 2
print(map2, symbols)
if map2 == map: break
map = map2
- Output:
_###_##_#_#_#_#__#____________ _#_#####_#_#_#________________ __##___##_#_#_________________ __##___###_#__________________ __##___#_##___________________ __##____###___________________ __##____#_#___________________ __##_____#____________________ __##__________________________ __##__________________________
Using a string character counting method:
import strutils
const
s_init: string = "_###_##_#_#_#_#__#__"
arrLen: int = 20
var q0: string = s_init & repeat('_',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 = repeat('_',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)
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
Using nested functions and method calling style:
proc cellAutomata =
proc evolveInto(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.evolveInto t
swap t, x
cellAutomata()
- Output:
.ooo.oo.o.o.o.o..o.. .o.ooooo.o.o.o...... ..oo...oo.o.o....... ..oo...ooo.o........ ..oo...o.oo......... ..oo....ooo......... ..oo....o.o......... ..oo.....o.......... ..oo................ ..oo................
OCaml
let get g i =
try g.(i)
with _ -> 0
let next_cell g i =
match get g (i-1), get g (i), get g (i+1) with
| 0, 0, 0 -> 0
| 0, 0, 1 -> 0
| 0, 1, 0 -> 0
| 0, 1, 1 -> 1
| 1, 0, 0 -> 0
| 1, 0, 1 -> 1
| 1, 1, 0 -> 1
| 1, 1, 1 -> 0
| _ -> assert(false)
let next g =
let old_g = Array.copy g in
for i = 0 to pred(Array.length g) do
g.(i) <- (next_cell old_g i)
done
let print_g g =
for i = 0 to pred(Array.length g) do
if g.(i) = 0
then print_char '_'
else print_char '#'
done;
print_newline()
put the code above in a file named "life.ml", and then use it in the ocaml toplevel like this:
#use "life.ml" ;;
let iter n g =
for i = 0 to n do
Printf.printf "Generation %d: " i; print_g g;
next g;
done
;;
let g_of_string str =
let f = (function '_' -> 0 | '#' -> 1 | _ -> assert false) in
Array.init (String.length str) (fun i -> f str.[i])
;;
# iter 9 (g_of_string "_###_##_#_#_#_#__#__") ;;
Generation 0: _###_##_#_#_#_#__#__
Generation 1: _#_#####_#_#_#______
Generation 2: __##___##_#_#_______
Generation 3: __##___###_#________
Generation 4: __##___#_##_________
Generation 5: __##____###_________
Generation 6: __##____#_#_________
Generation 7: __##_____#__________
Generation 8: __##________________
Generation 9: __##________________
- : unit = ()
Oforth
: nextGen( l )
| i s |
l byteSize dup ->s String newSize
s loop: i [
i 1 if=: [ 0 ] else: [ i 1- l byteAt '#' = ]
i l byteAt '#' = +
i s if=: [ 0 ] else: [ i 1+ l byteAt '#' = ] +
2 if=: [ '#' ] else: [ '_' ] over add
]
;
: gen( l n -- )
l dup .cr #[ nextGen dup .cr ] times( n ) drop ;- Output:
"_###_##_#_#_#_#__#__" 10 gen _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________ ok
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- 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.
step(v)=my(u=vector(#v),k);u[1]=v[1]&v[2];u[#u]=v[#v]&v[#v-1];for(i=2,#v-1,k=v[i-1]+v[i+1];u[i]=if(v[i],k==1,k==2));u;To simulate a run of 10 generations of the automaton, the function above can be put in a loop that spawns a new generation as a function of nth generations passed (n=0 is the initial state):
cur = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]; for(n=0, 9, print(cur); cur = step(cur));Output
[0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]
[0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Pascal
program Test;
{$IFDEF FPC}{$MODE DELPHI}{$ELSE}{$APPTYPE}{$ENDIF}
uses
sysutils;
const
cCHAR: array[0..1] of char = ('_','#');
type
TRow = array of byte;
function ConvertToRow(const s:string):tRow;
var
i : NativeInt;
Begin
i := length(s);
setlength(Result,length(s));
For i := i downto 0 do
result[i-1]:= ORD(s[i]=cChar[1]);
end;
function OutRow(const row:tRow):string;
//create output string
var
i: NativeInt;
Begin
i := length(row);
setlength(result,i);
For i := i downto 1 do
result[i]:= cChar[row[i-1]];
end;
procedure NextRow(row:pByteArray;MaxIdx:NativeInt);
//compute next row in place by the using a small storage for the
//2 values, that would otherwise be overridden
var
leftValue,Value: NativeInt;
i,trpCnt: NativeInt;
Begin
leftValue := 0;
trpCnt := row[0]+row[1];
i := 0;
while i < MaxIdx do
Begin
Value := row[i];
//the rule for survive : PopCnt == 2
row[i] := ORD(trpCnt= 2);
//reduce popcnt of element before
dec(trpCnt,leftValue);
//goto next element
inc(i);
leftValue := Value;
//increment popcnt by right element
inc(trpCnt,row[i+1]);
//move to next position in ring buffer
end;
row[MaxIdx] := ORD(trpCnt= 2);
end;
const
TestString: string=' ### ## # # # # # ';
var
s: string;
row:tRow;
i: NativeInt;
begin
s := Teststring;
row:= ConvertToRow(s);
For i := 0 to 9 do
Begin
writeln(OutRow(row));
NextRow(@row[0],High(row));
end;
end.
- Output:
__###_##_#_#_#_#__#__ __#_#####_#_#_#______ ___##___##_#_#_______ ___##___###_#________ ___##___#_##_________ ___##____###_________ ___##____#_#_________ ___##_____#__________ ___##________________
___##________________
Perl
Use regexp to extract and substitute cells while the string changes
Convert cells to zeros and ones to set complement state
$_="_###_##_#_#_#_#__#__\n";
do {
y/01/_#/;
print;
y/_#/01/;
s/(?<=(.))(.)(?=(.))/$1 == $3 ? $1 ? 1-$2 : 0 : $2/eg;
} while ($x ne $_ and $x=$_);
Use hash for complement state
$_="_###_##_#_#_#_#__#__\n";
%h=qw(# _ _ #);
do {
print;
s/(?<=(.))(.)(?=(.))/$1 eq $3 ? $1 eq "_" ? "_" : $h{$2} : $2/eg;
} while ($x ne $_ and $x=$_);
- Output:
for both versions
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
Phix
Ludicrously optimised:
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
- Output:
"_###_##_#_#_#_#__#__" "_#_#####_#_#_#______" "__##___##_#_#_______" "__##___###_#________" "__##___#_##_________" "__##____###_________" "__##____#_#_________" "__##_____#__________" "__##________________" "__##________________"
And of course I had to have a crack at that Sierpinski_Triangle:
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
- Output:
"________________________#________________________" "_______________________#_#_______________________" "______________________#___#______________________" "_____________________#_#_#_#_____________________" "____________________#_______#____________________" "___________________#_#_____#_#___________________" "__________________#___#___#___#__________________" "_________________#_#_#_#_#_#_#_#_________________" "________________#_______________#________________" "_______________#_#_____________#_#_______________" "______________#___#___________#___#______________" "_____________#_#_#_#_________#_#_#_#_____________" "____________#_______#_______#_______#____________" "___________#_#_____#_#_____#_#_____#_#___________" "__________#___#___#___#___#___#___#___#__________" "_________#_#_#_#_#_#_#_#_#_#_#_#_#_#_#_#_________" "________#_______________________________#________" "_______#_#_____________________________#_#_______" "______#___#___________________________#___#______" "_____#_#_#_#_________________________#_#_#_#_____" "____#_______#_______________________#_______#____" "___#_#_____#_#_____________________#_#_____#_#___" "__#___#___#___#___________________#___#___#___#__" "_#_#_#_#_#_#_#_#_________________#_#_#_#_#_#_#_#_"
Phixmonti
0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 stklen var w
w tolist 0 0 put
0 w 1 + repeat var x2
10 for
drop
w for
var j
j get 1 == if "#" else "_" endif print
j 1 - get var p1 j get swap j 1 + get rot p1 + + 2 ==
x2 swap j set var x2
endfor
nl
drop x2
endforPicat
go =>
% _ # # # _ # # _ # _ # _ # _ # _ _ # _ _
S = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0],
println(init=S),
run_ca(S),
nl,
println("Some random inits:"),
_ = random2(),
foreach(N in [5,10,20,50])
S2 = [random() mod 2 : _I in 1..N],
run_ca(S2),
nl
end.
%
% Run a CA and show the result.
%
% rule/1 is the default
run_ca(S) =>
run_ca(S,rule).
run_ca(S,Rules) =>
Len = S.length,
All := [S],
Seen = new_map(), % detect fixpoint and cycle
while (not Seen.has_key(S))
Seen.put(S,1),
T = [S[1]] ++ [apply(Rules, slice(S,I-1,I+1)) : I in 2..Len-1] ++ [S[Len]],
All := All ++ [T],
S := T
end,
foreach(A in All) println(A.convert()) end,
writeln(len=All.length).
% Convert:
% 0->"_"
% 1->"#"
convert(L) = Res =>
B = "_#",
Res = [B[L[I]+1] : I in 1..L.length].
% the rules
rule([0,0,0]) = 0. %
rule([0,0,1]) = 0. %
rule([0,1,0]) = 0. % Dies without enough neighbours
rule([0,1,1]) = 1. % Needs one neighbour to survive
rule([1,0,0]) = 0. %
rule([1,0,1]) = 1. % Two neighbours giving birth
rule([1,1,0]) = 1. % Needs one neighbour to survive
rule([1,1,1]) = 0. % Starved to death.- Output:
init = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ len = 10 Some random inits: _###_ _#_#_ __#__ _____ _____ len = 5 _#___##_#_ _____###__ _____#_#__ ______#___ __________ __________ len = 6 ###__####_#___#___## #_#__#__##________## ##______##________## ##______##________## len = 4 ______###_#_#___####__#_______#__#___#_####__#_### ______#_##_#____#__#__________________##__#___##_# _______####___________________________##______#### _______#__#___________________________##______#__# ______________________________________##_________# ______________________________________##_________# len = 6
The program is fairly general. Here's the additional code for the rule 30 CA.
go2 =>
N = 4,
Ns = [0 : _ in 1..N],
S = Ns ++ [1] ++ Ns,
run_ca(S, rule30).
% The rules for rule 30
rule30([0,0,0]) = 0.
rule30([0,0,1]) = 1.
rule30([0,1,0]) = 1.
rule30([0,1,1]) = 1.
rule30([1,0,0]) = 1.
rule30([1,0,1]) = 0.
rule30([1,1,0]) = 0.
rule30([1,1,1]) = 0.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 "_") ) ) ) )- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
Prolog
Works ith SWI-Prolog.
one_dimensional_cellular_automata(L) :-
maplist(my_write, L), nl,
length(L, N),
length(LN, N),
% there is a 0 before the beginning
compute_next([0 |L], LN),
( L \= LN -> one_dimensional_cellular_automata(LN); true).
% All the possibilites
compute_next([0, 0, 0 | R], [0 | R1]) :-
compute_next([0, 0 | R], R1).
compute_next([0, 0, 1 | R], [0 | R1]) :-
compute_next([0, 1 | R], R1).
compute_next([0, 1, 0 | R], [0 | R1]) :-
compute_next([1, 0 | R], R1).
compute_next([0, 1, 1 | R], [1 | R1]) :-
compute_next([1, 1 | R], R1).
compute_next([1, 0, 0 | R], [0 | R1]) :-
compute_next([0, 0 | R], R1).
compute_next([1, 0, 1 | R], [1 | R1]) :-
compute_next([0, 1 | R], R1).
compute_next([1, 1, 0 | R], [1 | R1]) :-
compute_next([1, 0 | R], R1).
compute_next([1, 1, 1 | R], [0 | R1]) :-
compute_next([1, 1 | R], R1).
% the last four possibilies =>
% we consider that there is à 0 after the end
complang jq># The 1-d cellular automaton:
def next:
# Conveniently, jq treats null as 0 when it comes to addition
# so there is no need to fiddle with the boundaries
. as $old
| reduce range(0; length) as $i
([];
($old[$i-1] + $old[$i+1]) as $s
| if $s == 0 then .[$i] = 0
elif $s == 1 then .[$i] = (if $old[$i] == 1 then 1 else 0 end)
else .[$i] = (if $old[$i] == 1 then 0 else 1 end)
end);
# pretty-print an array:
def pp: reduce .[] as $i (""; . + (if $i == 0 then " " else "*" end));
# continue until quiescence:
def go: recurse(. as $prev | next | if . == $prev then empty else . end) | pp;
# Example:
[0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] | goute_next([0, 0], [0]).
compute_next([1, 0], [0]).
compute_next([0, 1], [0]).
compute_next([1, 1], [1]).
my_write(0) :-
write(.).
my_write(1) :-
write(#).
one_dimensional_cellular_automata :-
L = [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0],
one_dimensional_cellular_automata(L).
- Output:
?- one_dimensional_cellular_automata. .###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ true .
Python
Procedural
Python: Straightforward interpretation of spec
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))
- 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.
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
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.
>>> gen = [ch == '#' for ch in '_###_##_#_#_#_#__#__']
>>> for n in range(10):
print(''.join('#' if cell else '_' for cell in gen))
gen = [0] + gen + [0]
gen = [sum(gen[m:m+3]) == 2 for m in range(len(gen)-2)]
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
__##________________
__##________________
>>>
Composition of pure functions
Interpreting the rule shown in the task description as Wolfram rule 104, and generalising enough to allow for other rules of this kind:
'''Cellular Automata'''
from itertools import islice, repeat
from functools import reduce
from random import randint
# nextRowByRule :: Int -> [Bool] -> [Bool]
def nextRowByRule(intRule):
'''A row of booleans derived by Wolfram rule n
from another boolean row of the same length.
'''
# step :: (Bool, Bool, Bool) -> Bool
def step(l, x, r):
return bool(intRule & 2**intFromBools([l, x, r]))
# go :: [Bool] -> [Bool]
def go(xs):
return [False] + list(map(
step,
xs, xs[1:], xs[2:]
)) + [False]
return go
# intFromBools :: [Bool] -> Int
def intFromBools(xs):
'''Integer derived by binary interpretation
of a list of booleans.
'''
def go(b, pn):
power, n = pn
return (2 * power, n + power if b else n)
return foldr(go)([1, 0])(xs)[1]
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Samples of Wolfram rule evolutions.
'''
print(
unlines(map(showRuleSample, [104, 30, 110]))
)
# ----------------------- DISPLAY ------------------------
# showRuleSample :: Int -> String
def showRuleSample(intRule):
'''16 steps in the evolution
of a given Wolfram rule.
'''
return 'Rule ' + str(intRule) + ':\n' + (
unlines(map(
showCells,
take(16)(
iterate(nextRowByRule(intRule))(
onePixelInLineOf(64) if (
bool(randint(0, 1))
) else randomPixelsInLineOf(64)
)
)
))
)
# boolsFromInt :: Int -> [Bool]
def boolsFromInt(n):
'''List of booleans derived by binary
decomposition of an integer.
'''
def go(x):
return Just((x // 2, bool(x % 2))) if x else Nothing()
return unfoldl(go)(n)
# nBoolsFromInt :: Int -> Int -> [Bool]
def nBoolsFromInt(n):
'''List of bools, left-padded to given length n,
derived by binary decomposition of an integer x.
'''
def go(n, x):
bs = boolsFromInt(x)
return list(repeat(False, n - len(bs))) + bs
return lambda x: go(n, x)
# onePixelInLineOf :: Int -> [Bool]
def onePixelInLineOf(n):
'''A row of n (mainly False) booleans,
with a single True value in the middle.
'''
return nBoolsFromInt(n)(
2**(n // 2)
)
# randomPixelsInLineOf :: Int -> [Bool]
def randomPixelsInLineOf(n):
'''A row of n booleans with pseudorandom values.
'''
return [bool(randint(0, 1)) for _ in range(1, 1 + n)]
# showCells :: [Bool] -> String
def showCells(xs):
'''A block string representation of a list of booleans.
'''
return ''.join([chr(9608) if x else ' ' for x in xs])
# ----------------------- GENERIC ------------------------
# Just :: a -> Maybe a
def Just(x):
'''Constructor for an inhabited Maybe (option type) value.
Wrapper containing the result of a computation.
'''
return {'type': 'Maybe', 'Nothing': False, 'Just': x}
# Nothing :: () -> Maybe a
def Nothing():
'''Constructor for an empty Maybe (option type) value.
Empty wrapper returned where a computation is not possible.
'''
return {'type': 'Maybe', 'Nothing': True}
# foldr :: (a -> b -> b) -> b -> [a] -> b
def foldr(f):
'''Right to left reduction of a list,
using the binary operator f, and
starting with an initial accumulator value.
'''
def g(a, x):
return f(x, a)
return lambda acc: lambda xs: reduce(
g, xs[::-1], acc
)
# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''
def go(x):
v = x
while True:
yield v
v = f(v)
return go
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
def go(xs):
return (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
return go
# unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
'''Dual to reduce or foldl.
Where these reduce a list to a summary value, unfoldl
builds a list from a seed value.
Where f returns Just(a, b), a is appended to the list,
and the residual b is used as the argument for the next
application of f.
When f returns Nothing, the completed list is returned.
'''
def go(v):
x, r = v, v
xs = []
while True:
mb = f(x)
if mb.get('Nothing'):
return xs
else:
x, r = mb.get('Just')
xs.insert(0, r)
return xs
return go
# unlines :: [String] -> String
def unlines(xs):
'''A single string formed by the intercalation
of a list of strings with the newline character.
'''
return '\n'.join(xs)
# MAIN -------------------------------------------------
if __name__ == '__main__':
main()
- Output:
Rule 104:
█ █ ████ ██ █ █ █ █ █ ██ █████ ██ ██ █ ██
█ █ ██ █ █ ███ █ ████ ██ ███
██ █ ██ █ █ █ ██ █ █
██ ████ ██ █
██ █ █ ██
██ ██
██ ██
██ ██
██ ██
██ ██
██ ██
██ ██
██ ██
██ ██
██ ██
██ ██
Rule 30:
█
███
██ █
██ ████
██ █ █
██ ████ ███
██ █ █ █
██ ████ ██████
██ █ ███ █
██ ████ ██ █ ███
██ █ █ ████ ██ █
██ ████ ██ █ █ ████
██ █ ███ ██ ██ █ █
██ ████ ██ ███ ███ ██ ███
██ █ █ ███ █ ███ █ █
██ ████ ██ █ █ █████ ███████
Rule 110:
█ █ ██ ██ ██ █ █ ██ ███ █ █ ███ ██ ██ █ █ █
██ ██████ ███ ████ ███ ██ ███████ █ ██████ ██ ██ ██
█████ ███ ███ ███ ██████ ███ ██ █ ███ ███ ███
█ █ ██ ███ █ ██ ███ █ ██ █ ███ ██ ██ █ ██ ███ █
█ ██ █████ ████████ █ ██ █████ ██ █ █████████████ ███
█ ███ ██ ███ ███ ███ ██ ██████ ██ ███ █
███ ████ ██ █ ██ █ ██ █ ███ ██ ████ ██ ███
█ ███ █ █████ ████████████ █ ███ ██ █ █████ █
███ █ ████ █ ██ █████ █ ███ ██ ██ ███
█ █████ █ ██ ███ ██ ███ ██ ████ ███ ██ █
███ █ ██ ███ ██ █ ███ ██ ██████ █ ██ █ █████
█ █ ███████ ██████ ██ █ █████ █ ██ ███████ █
███ ██ ███ █ ███████ █ █████ ██ █ ██
█ ████ ██ █ ██ ██ █ ██ ██ █ ███ ██ ███
███ █ █████ ███ ███ ██ ███ ███ ██ ██ █ █████ █
█ █ ██ ██ █ ██ █ ██ █ █████ ███ █ ███ █████ ██ ███
Quackery
[ stack 0 ] is cells ( --> s )
[ dup size cells replace
0 swap witheach
[ char # =
| 1 << ] ] is setup ( $ --> n )
[ 0 swap
cells share times
[ dup i >> 7 &
[ table 0 0 0 1 0 1 1 0 ]
rot 1 << | swap ]
drop 1 << ] is nextline ( n --> n )
[ cells share times
[ dup i 1+ bit &
iff [ char # ]
else [ char _ ]
emit ]
cr drop ] is echoline ( n --> )
[ setup
[ dup echoline
dup nextline
tuck = until ]
echoline ] is automate ( $ --> )
$ "_###_##_#_#_#_#__#__" automate- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________
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")
}
- Output:
1 _##_____####_#___#_#__ 2 _##_____#__##_____#___ 3 _##________##_________ 4 _##________##_________ 5 _##________##_________ 6 _##________##_________ 7 _##________##_________ 8 _##________##_________ 9 _##________##_________ 10 _##________##_________
Racket
#lang racket
(define (update cells)
(for/list ([crowding (map +
(append '(0) (drop-right cells 1))
cells
(append (drop cells 1) '(0)))])
(if (= 2 crowding) 1 0)))
(define (life-of cells time)
(unless (zero? time)
(displayln cells)
(life-of (update cells) (sub1 time))))
(life-of '(0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0)
10)
#| (0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0)
(0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0)
(0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
(0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0) |#
Below is an alternative implementation using graphical output in the Racket REPL. It works with DrRacket and Emacs + Geiser.
#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)
Raku
(formerly 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.
class Automaton {
has $.rule;
has @.cells;
has @.code = $!rule.fmt('%08b').flip.comb».Int;
method gist { "|{ @!cells.map({+$_ ?? '#' !! ' '}).join }|" }
method succ {
self.new: :$!rule, :@!code, :cells(
@!code[
4 «*« @!cells.rotate(-1)
»+« 2 «*« @!cells
»+« @!cells.rotate(1)
]
)
}
}
# The rule proposed for this task is rule 0b01101000 = 104
my @padding = 0 xx 5;
my Automaton $a .= new:
rule => 104,
cells => flat @padding, '111011010101'.comb, @padding
;
say $a++ for ^10;
# Rule 104 is not particularly interesting so here is [[wp:Rule 90|Rule 90]],
# which shows a [[wp:Sierpinski Triangle|Sierpinski Triangle]].
say '';
@padding = 0 xx 25;
$a = Automaton.new: :rule(90), :cells(flat @padding, 1, @padding);
say $a++ for ^20;
- Output:
| ### ## # # # | | # ##### # # | | ## ## # | | ## ### | | ## # # | | ## # | | ## | | ## | | ## | | ## | | # | | # # | | # # | | # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # # # | | # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # |
Red
Red [
Purpose: "One-dimensional cellular automata"
Author: "Joe Smith"
]
vals: [0 1 0]
kill: [[0 0] [#[none] 0] [0 #[none]]]
evo: function [petri] [
new-petri: copy petri
while [petri/1] [
if all [petri/-1 = 1 petri/2 = 1] [new-petri/1: select vals petri/1]
if find/only kill reduce [petri/-1 petri/2] [new-petri/1: 0]
petri: next petri new-petri: next new-petri
]
petri: head petri new-petri: head new-petri
clear insert petri new-petri
]
display: function [petri] [
print replace/all (replace/all to-string petri "0" "_") "1" "#"
petri
]
loop 10 [
evo display [1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0]
]
- Output:
###_##_#_#_#_#__#_ #_#####_#_#_#_____ _##___##_#_#______ _##___###_#_______ _##___#_##________ _##____###________ _##____#_#________ _##_____#_________ _##_______________ _##_______________
Refal
$ENTRY Go {
, ' ### ## # # # # # ': e.State
= <Run <Table> 10 e.State>;
};
Table {
= (((' ') ' ')
((' #') ' ')
((' # ') ' ')
((' ##') '#')
(('# ') ' ')
(('# #') '#')
(('## ') '#')
(('###') ' '));
};
Run {
t.Table 0 e.X = ;
t.Table s.Steps e.X =
<Prout e.X>
<Run t.Table <- s.Steps 1> <DoStep t.Table e.X>>;
};
DoStep {
t.Table e.X = <Step1 t.Table ' ' e.X ' '>;
};
Step1 {
t.Table s.1 s.2 s.3 e.R,
<Lookup t.Table s.1 s.2 s.3>: e.Next,
e.R: {
= e.Next;
e.R = e.Next <Step1 t.Table s.2 s.3 e.R>;
};
}
Lookup {
(e.A ((e.X)e.Y) e.B) e.X = e.Y;
};- Output:
### ## # # # # # # ##### # # # ## ## # # ## ### # ## # ## ## ### ## # # ## # ## ##
Retro
# 1D Cellular Automota
Assume an array of cells with an initial distribution of live and
dead cells, and imaginary cells off the end of the array having
fixed values.
Cells in the next generation of the array are calculated based on
the value of the cell and its left and right nearest neighbors in
the current generation.
If, in the following table, a live cell is represented by 1 and a
dead cell by 0 then to generate the value of the cell at a particular
index in the array of cellular values you use the following table:
000 -> 0 #
001 -> 0 #
010 -> 0 # Dies without enough neighbours
011 -> 1 # Needs one neighbour to survive
100 -> 0 #
101 -> 1 # Two neighbours giving birth
110 -> 1 # Needs one neighbour to survive
111 -> 0 # Starved to death.
I had originally written an implementation of this in RETRO 11.
For RETRO 12 I took advantage of new language features and some
further considerations into the rules for this task.
The first word, `string,` inlines a string to `here`. I'll use
this to setup the initial input.
~~~
:string, (s-) [ , ] s:for-each #0 , ;
~~~
The next two lines setup an initial generation and a buffer for
the evolved generation. In this case, `This` is the current
generation and `Next` reflects the next step in the evolution.
~~~
'This d:create
'.###.##.#.#.#.#..#.. string,
'Next d:create
'.................... string,
~~~
I use `display` to show the current generation.
~~~
:display (-)
&This s:put nl ;
~~~
As might be expected, `update` copies the `Next` generation to
the `This` generation, setting things up for the next cycle.
~~~
:update (-)
&Next &This dup s:length copy ;
~~~
The word `group` extracts a group of three cells. This data will
be passed to `evolve` for processing.
~~~
:group (a-nnn)
[ fetch ]
[ n:inc fetch ]
[ n:inc n:inc fetch ] tri ;
~~~
I use `evolve` to decide how a cell should change, based on its
initial state with relation to its neighbors.
In the prior implementation this part was much more complex as I
tallied things up and had separate conditions for each combination.
This time I take advantage of the fact that only cells with two
neighbors will be alive in the next generation. So the process is:
- take the data from `group`
- compare to `$#` (for living cells)
- add the flags
- if the result is `#-2`, the cell should live
- otherwise it'll be dead
~~~
:evolve (nnn-c)
[ $# eq? ] tri@ + +
#-2 eq? [ $# ] [ $. ] choose ;
~~~
For readability I separated out the next few things. `at` takes an
index and returns the address in `This` starting with the index.
~~~
:at (n-na)
&This over + ;
~~~
The `record` word adds the evolved value to a buffer. In this case
my `generation` code will set the buffer to `Next`.
~~~
:record (c-)
buffer:add n:inc ;
~~~
And now to tie it all together. Meet `generation`, the longest bit
of code in this sample. It has several bits:
- setup a new buffer pointing to `Next`
- this also preserves the old buffer
- setup a loop for each cell in `This`
- initial loop index at -1, to ensure proper dummy state for first cell
- get length of `This` generation
- perform a loop for each item in the generation, updating `Next` as it goes
- copy `Next` to `This` using `update`.
~~~
:generation (-)
[ &Next buffer:set
#-1 &This s:length
[ at group evolve record ] times drop
update
] buffer:preserve ;
~~~
The last bit is a helper. It takes a number of generations and displays
the state, then runs a `generation`.
~~~
:generations (n-)
[ display generation ] times ;
~~~
And a text. The output should be:
.###.##.#.#.#.#..#..
.#.#####.#.#.#......
..##...##.#.#.......
..##...###.#........
..##...#.##.........
..##....###.........
..##....#.#.........
..##.....#..........
..##................
..##................
~~~
#10 generations
~~~REXX
This REXX version will show (as a default) 40 generations, or less if the generations of cellular automata repeat.
/*REXX program generates & displays N generations of one─dimensional cellular automata. */
parse arg $ gens . /*obtain optional arguments from the CL*/
if $=='' | $=="," then $=001110110101010 /*Not specified? Then use the default.*/
if gens=='' | gens=="," then gens=40 /* " " " " " " */
do #=0 for gens /* process the one-dimensional cells.*/
say " generation" right(#,length(gens)) ' ' translate($, "#·", 10)
@=0 /* [↓] generation.*/
do j=2 for length($) - 1; x=substr($, j-1, 3) /*obtain the cell.*/
if x==011 | x==101 | x==110 then @=overlay(1, @, j) /*the cell lives. */
else @=overlay(0, @, j) /* " " dies. */
end /*j*/
if $==@ then do; say right('repeats', 40); leave; end /*does it repeat? */
$=@ /*now use the next generation of cells.*/
end /*#*/ /*stick a fork in it, we're all done. */
output when using the default input:
generation 0 ··###·##·#·#·#·
generation 1 ··#·#####·#·#··
generation 2 ···##···##·#···
generation 3 ···##···###····
generation 4 ···##···#·#····
generation 5 ···##····#·····
generation 6 ···##··········
repeats
Ring
# Project : One-dimensional cellular automata
rule = ["0", "0", "0", "1", "0", "1", "1", "0"]
now = "01110110101010100100"
for generation = 0 to 9
see "generation " + generation + ": " + now + nl
nxt = ""
for cell = 1 to len(now)
str = "bintodec(" + '"' +substr("0"+now+"0", cell, 3) + '"' + ")"
eval("p=" + str)
nxt = nxt + rule[p+1]
next
temp = nxt
nxt = now
now = temp
next
func bintodec(bin)
binsum = 0
for n=1 to len(bin)
binsum = binsum + number(bin[n]) *pow(2, len(bin)-n)
next
return binsumOutput:
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
RPL
Rather than assuming fixed values for cells beyond borders, it has been decided to make the board 'circular', as it is the case in many 2D versions. A new generation is directly derived from the output string of the previous generation.
≪ 1 10 START
DUP DUP 1 1 SUB
OVER DUP SIZE DUP SUB ROT + SWAP +
{ "_##" "#_#" "##_" }
→ gen lives
≪ "" 2 gen SIZE 1 - FOR j
lives gen j 1 - DUP 2 + SUB POS "#" "_" IFTE +
NEXT
≫
NEXT
≫
'CELLS' STO
"_###_##_#_#_#_#__#__" CELLS
- Output:
10: _###_##_#_#_#_#__#__ 9: _#_#####_#_#_#______ 8: __##___##_#_#_______ 7: __##___###_#________ 6: __##___#_##_________ 5: __##____###_________ 4: __##____#_#_________ 3: __##_____#__________ 2: __##________________ 1: __##________________
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
- Output:
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................
Rust
fn get_new_state(windowed: &[bool]) -> bool {
match windowed {
[false, true, true] | [true, true, false] => true,
_ => false
}
}
fn next_gen(cell: &mut [bool]) {
let mut v = Vec::with_capacity(cell.len());
v.push(cell[0]);
for i in cell.windows(3) {
v.push(get_new_state(i));
}
v.push(cell[cell.len() - 1]);
cell.copy_from_slice(&v);
}
fn print_cell(cell: &[bool]) {
for v in cell {
print!("{} ", if *v {'#'} else {' '});
}
println!();
}
fn main() {
const MAX_GENERATION: usize = 10;
const CELLS_LENGTH: usize = 30;
let mut cell: [bool; CELLS_LENGTH] = rand::random();
for i in 1..=MAX_GENERATION {
print!("Gen {:2}: ", i);
print_cell(&cell);
next_gen(&mut cell);
}
}
Scala
def cellularAutomata(s: String) = {
def it = Iterator.iterate(s) ( generation =>
("_%s_" format generation).iterator
sliding 3
map (_ count (_ == '#'))
map Map(2 -> "#").withDefaultValue("_")
mkString
)
(it drop 1) zip it takeWhile Function.tupled(_ != _) map (_._2) foreach println
}
Sample:
scala> cellularAutomata("_###_##_#_#_#_#__#__")
_###_##_#_#_#_#__#__
_#_#####_#_#_#______
__##___##_#_#_______
__##___###_#________
__##___#_##_________
__##____###_________
__##____#_#_________
__##_____#__________
Scheme
Works with: Scheme version RRS
(define (next-generation left petri-dish right)
(if (null? petri-dish)
(list)
(cons (if (= (+ left
(car petri-dish)
(if (null? (cdr petri-dish))
right
(cadr petri-dish)))
2)
1
0)
(next-generation (car petri-dish) (cdr petri-dish) right))))
(define (display-evolution petri-dish generations)
(if (not (zero? generations))
(begin (display petri-dish)
(newline)
(display-evolution (next-generation 0 petri-dish 0)
(- generations 1)))))
(display-evolution (list 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0) 10)
Output:
(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.
$ include "seed7_05.s7i";
const string: start is "_###_##_#_#_#_#__#__";
const proc: main is func
local
var string: g0 is start;
var string: g1 is start;
var integer: generation is 0;
var integer: i is 0;
begin
writeln(g0);
for generation range 0 to 9 do
for i range 2 to pred(length(g0)) do
if g0[i-1] <> g0[i+1] then
g1 @:= [i] g0[i];
elsif g0[i] = '_' then
g1 @:= [i] g0[i-1];
else
g1 @:= [i] '_'
end if;
end for;
writeln(g1);
g0 := g1;
end for;
end func;Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
SequenceL
import <Utilities/Conversion.sl>;
main(args(2)) :=
run(args[1], stringToInt(args[2])) when size(args) = 2
else
"Usage error: exec <initialCells> <generations>";
stringToCells(string(1))[i] := 0 when string[i] = '_' else 1;
cellsToString(cells(1))[i] := '#' when cells[i] = 1 else '_';
run(cellsString(1), generations) :=
runHelper(stringToCells(cellsString), generations, cellsString);
runHelper(cells(1), generations, result(1)) :=
let
nextCells := step(cells);
in
result when generations = 0
else
runHelper(nextCells, generations - 1,
result ++ "\n" ++ cellsToString(nextCells));
step(cells(1))[i] :=
let
left := cells[i-1] when i > 1 else 0;
right := cells[i + 1] when i < size(cells) else 0;
in
1 when (left + cells[i] + right) = 2
else
0;- Output:
"_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________"
Sidef
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;
}
- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
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;
}- Output:
| ### ## # # # | | # ##### # # | | ## ## # | | ## ### | | ## # # | | ## # | | ## | | ## | | ## | | ## |
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 $array
}Uiua
Based on the example code on the Uiua homepage.
Uses the provided Rule 104. More interesting rules are 105, 110, 30, 90 etc.
Rule ← /+⊞= ⊓(⊚⋯|°⋯⇌◫3⇌ ⊂⊂0:0)
[⍥(⁅⚂)200] # Init
⇌[⍥(Rule104.)⌊÷2⧻.] # Run
▽⟜(≡▽)4 # Scale upUrsala
Three functions are defined. Rule takes a neighborhood of three cells to the succeeding value of the middle one, step takes a list of cells to its successor by applying the rule across a sliding window, and evolve takes an initial list of cells to a list of those evolving from it according to the rule. The cells are maintained as a list of booleans (0 and &) but are converted to characters for presentation in the example code.
#import std
#import nat
rule = -$<0,0,0,&,0,&,&,0>@rSS zipp0*ziD iota8
step = rule*+ swin3+ :/0+ --<0>
evolve "n" = @iNC ~&x+ rep"n" ^C/step@h ~&
#show+
example = ~&?(`#!,`.!)** evolve10 <0,&,&,&,0,&,&,0,&,0,&,0,&,0,0,&,0,0>output:
.###.##.#.#.#..#.. .#.#####.#.#...... ..##...##.#....... ..##...###........ ..##...#.#........ ..##....#......... ..##.............. ..##.............. ..##.............. ..##.............. ..##..............
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.
IT("Gen 0: ..###.##.#.#.#.#..#.....") // initial pattern
#9 = Cur_Col
for (#8 = 1; #8 < 10; #8++) { // 10 generations
Goto_Col(7)
Reg_Empty(20)
while (Cur_Col < #9-1) {
if (Match("|{##|!#,#.#,|!###}")==0) {
Reg_Set(20, "#", APPEND)
} else {
Reg_Set(20, ".", APPEND)
}
Char
}
EOL IN
IT("Gen ") Num_Ins(#8, LEFT+NOCR) IT(": ")
Reg_Ins(20)
}Sample output:
Gen 0: ..###.##.#.#.#.#..#.....
Gen 1: ..#.#####.#.#.#.........
Gen 2: ...##...##.#.#..........
Gen 3: ...##...###.#...........
Gen 4: ...##...#.##............
Gen 5: ...##....###............
Gen 6: ...##....#.#............
Gen 7: ...##.....#.............
Gen 8: ...##...................
Gen 9: ...##...................Wart
Simple
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) bOutput 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.
def (uca l) # new datatype: Uni-dimensional Cellular Automaton
(tag uca (list l len.l))
def (len l) :case (isa uca l) # how to compute its length
rep.l.1
defcoerce uca list # how to convert it to a list
(fn(_) rep._.0)
def (pr l) :case (isa uca l) # how to print it
each x l # transparently coerces to a list for iterating over
pr (if x "#" "_")
# (l i) returns ith cell when l is a uca, and nil when i is out-of-bounds
defcall uca (l i)
if (0 <= i < len.l)
rep.l.0.i
def (gens n l)
prn l
repeat n
zap! gen l
prn l
def (gen l)
uca+collect+for i 0 (i < len.l) ++i
yield (next (l i-1) l.i (l i+1))
# next state of b, given neighbors a and c
def (next a b c)
if (and a c) not.b
(or a c) bOutput 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)) _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ __##________________
Wren
var trans = "___#_##_"
var v = Fn.new { |cell, i| (cell[i] != "_") ? 1 : 0 }
var evolve = Fn.new { |cell, backup|
var len = cell.count - 2
var diff = 0
for (i in 1...len) {
/* use left, self, right as binary number bits for table index */
backup[i] = trans[v.call(cell, i - 1) * 4 + v.call(cell, i) * 2 + v.call(cell, i + 1)]
diff = diff + ((backup[i] != cell[i]) ? 1 : 0)
}
cell.clear()
cell.addAll(backup)
return diff != 0
}
var c = "_###_##_#_#_#_#__#__".toList
var b = "____________________".toList
while(true) {
System.print(c[1..-1].join())
if (!evolve.call(c,b)) break
}- Output:
###_##_#_#_#_#__#__ #_#####_#_#_#______ _##___##_#_#_______ _##___###_#________ _##___#_##_________ _##____###_________ _##____#_#_________ _##_____#__________ _##________________
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 then ^# else ^_);
CrLf(0);
New:= 0;
for I:= 30 downto 1 do
case Now>>(I-1) & 7 of %011, %101, %110: New:= New ! 1<<I other;
Now:= New;
];
]- Output:
_____###_##_#_#_#_#__#__________ _____#_#####_#_#_#______________ ______##___##_#_#_______________ ______##___###_#________________ ______##___#_##_________________ ______##____###_________________ ______##____#_#_________________ ______##_____#__________________ ______##________________________ ______##________________________
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 });
}chars:=T("_","#");
cells:="_###_##_#_#_#_#__#__".split("").apply('==("#")); //-->L(False,True,True,True,False...)
do(10){ cells.apply(chars.get).concat().println(); cells=life1D(cells); }Or, using strings instead of lists:
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();
}cells:="_###_##_#_#_#_#__#__";
do(10){ cells.println(); cells=life1D(cells); }- Output:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
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