Elementary cellular automaton
You are encouraged to solve this task according to the task description, using any language you may know.
An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Those three values can be encoded with three bits.
The rules of evolution are then encoded with eight bits indicating the outcome of each of the eight possibilities 111, 110, 101, 100, 011, 010, 001 and 000 in this order. Thus for instance the rule 13 means that a state is updated to 1 only in the cases 011, 010 and 000, since 13 in binary is 0b00001101.
- Task
Create a subroutine, program or function that allows to create and visualize the evolution of any of the 256 possible elementary cellular automaton of arbitrary space length and for any given initial state. You can demonstrate your solution with any automaton of your choice.
The space state should wrap: this means that the left-most cell should be considered as the right neighbor of the right-most cell, and reciprocally.
This task is basically a generalization of one-dimensional cellular automata.
- Related tasks
- See also
11l
V SIZE = 32
V LINES = SIZE I/ 2
V RULE = 90
F ruleTest(x)
R I :RULE [&] (1 << (7 [&] x)) != 0 {1} E 0
F bitVal(s, bit)
R I (s >> bit) [&] 1 != 0 {1} E 0
F evolve(&s)
V t = 0
t [|]= ruleTest((bitVal(s, 0) << 2) [|] (bitVal(s, :SIZE - 1) << 1) [|] bitVal(s, :SIZE - 2)) << (:SIZE - 1)
t [|]= ruleTest((bitVal(s, 1) << 2) [|] (bitVal(s, 0) << 1) [|] bitVal(s, :SIZE - 1))
L(i) 1 .< :SIZE - 1
t [|]= ruleTest((bitVal(s, i + 1) << 2) [|] (bitVal(s, i) << 1) [|] bitVal(s, i - 1)) << i
s = t
F show(state)
L(i) (:SIZE - 1 .. 0).step(-1)
print(‘ *’[bitVal(state, i)], end' ‘’)
print()
V state = 1 << LINES
print(‘Rule ’RULE)
L 1..LINES
show(state)
evolve(&state)- Output:
Rule 90
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Action!
DEFINE ROW_LEN="320"
DEFINE MAX_COL="319"
DEFINE MAX_ROW="191"
PROC GenerateMask(BYTE rule BYTE ARRAY mask)
BYTE i
FOR i=0 TO 7
DO
mask(i)=rule&1
rule==RSH 1
OD
RETURN
PROC InitRow(BYTE ARRAY row)
INT c
FOR c=0 TO MAX_COL
DO
row(c)=0
OD
row(ROW_LEN RSH 1)=1
RETURN
PROC DrawRow(BYTE ARRAY row BYTE y)
INT c
FOR c=0 TO MAX_COL
DO
Color=row(c)
Plot(c,y)
OD
RETURN
PROC CalcNextRow(BYTE ARRAY currRow,nextRow,mask)
INT c
BYTE v
v=currRow(MAX_COL) LSH 2
v==%currRow(0) LSH 1
v==%currRow(1)
nextRow(0)=mask(v)
FOR c=1 TO MAX_COL-1
DO
v==&3
v==LSH 1
v==%currRow(c+1)
nextRow(c)=mask(v)
OD
v==&3
v==LSH 1
v==%currRow(0)
nextRow(MAX_COL)=mask(v)
RETURN
PROC DrawRule(BYTE rule)
BYTE ARRAY row1(ROW_LEN),row2(ROW_LEN),mask(8)
BYTE ARRAY currRow,nextRow,tmp
BYTE y
GenerateMask(rule,mask)
currRow=row1
nextRow=row2
InitRow(currRow)
y=0
WHILE y<=MAX_ROW
DO
DrawRow(currRow,y)
CalcNextRow(currRow,nextRow,mask)
tmp=currRow currRow=nextRow nextRow=tmp
y==+1
OD
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Graphics(8+16)
Color=1
COLOR1=$0C
COLOR2=$02
DrawRule(30)
DO UNTIL CH#$FF OD
CH=$FF
RETURN- Output:
Screenshot from Atari 8-bit computer
Ada
with Ada.Text_IO;
procedure Elementary_Cellular_Automaton is
type t_Rule is new Integer range 0..2**8-1;
type t_State is array (Integer range <>) of Boolean;
Cell_Image : constant array (Boolean) of Character := ('.', '#');
function Image (State : in t_State) return String is
(Cell_Image(State(State'First)) &
(if State'Length <= 1 then ""
else Image(State(State'First+1..State'Last))));
-- More convenient representation of the rule
type t_RuleA is array (Boolean, Boolean, Boolean) of Boolean;
function Translate (Rule : in t_Rule) return t_RuleA is
-- Better not use Pack attribute and Unchecked_Conversion
-- because it would not be endianness independent...
Remain : t_Rule := Rule;
begin
return Answer : t_RuleA do
for K in Boolean loop
for J in Boolean loop
for I in Boolean loop
Answer(I,J,K) := (Remain mod 2 = 1);
Remain := Remain / 2;
end loop;
end loop;
end loop;
end return;
end Translate;
procedure Show_Automaton (Rule : in t_Rule;
Initial : in t_State;
Generations : in Positive) is
RuleA : constant t_RuleA := Translate(Rule);
Width : constant Positive := Initial'Length;
-- More convenient indices for neighbor wraparound with "mod"
subtype t_State0 is t_State (0..Width-1);
State : t_State0 := Initial;
New_State : t_State0;
begin
Ada.Text_IO.Put_Line ("Rule" & t_Rule'Image(Rule) & " :");
for Generation in 1..Generations loop
Ada.Text_IO.Put_Line (Image(State));
for Cell in State'Range loop
New_State(Cell) := RuleA(State((Cell-1) mod Width),
State(Cell),
State((Cell+1) mod Width));
end loop;
State := New_State;
end loop;
end Show_Automaton;
begin
Show_Automaton (Rule => 90,
Initial => (-10..-1 => False, 0 => True, 1..10 => False),
Generations => 15);
Show_Automaton (Rule => 30,
Initial => (-15..-1 => False, 0 => True, 1..15 => False),
Generations => 20);
Show_Automaton (Rule => 122,
Initial => (-12..-1 => False, 0 => True, 1..12 => False),
Generations => 25);
end Elementary_Cellular_Automaton;
- Output:
Rule 90 : ..........#.......... .........#.#......... ........#...#........ .......#.#.#.#....... ......#.......#...... .....#.#.....#.#..... ....#...#...#...#.... ...#.#.#.#.#.#.#.#... ..#...............#.. .#.#.............#.#. #...#...........#...# ##.#.#.........#.#.## .#....#.......#....#. #.#..#.#.....#.#..#.# #..##...#...#...##..# Rule 30 : ...............#............... ..............###.............. .............#..##............. ............####.##............ ...........#...#..##........... ..........###.####.##.......... .........#..#....#..##......... ........######..####.##........ .......#.....###...#..##....... ......###...#..##.####.##...... .....#..##.####.#....#..##..... ....####.#....#.##..####.##.... ...#...#.##..##..###...#..##... ..###.##..###.###..##.####.##.. .#..#..###..#...###.#....#..##. #######..#####.#..#.##..####.## ......###....#.####..###...#... .....#..##..##....###..##.###.. ....####.###.##..#..###.#...##. ...#...#...#..######..#.##.#.## Rule 122 : ............#............ ...........#.#........... ..........#.#.#.......... .........#.#.#.#......... ........#.#.#.#.#........ .......#.#.#.#.#.#....... ......#.#.#.#.#.#.#...... .....#.#.#.#.#.#.#.#..... ....#.#.#.#.#.#.#.#.#.... ...#.#.#.#.#.#.#.#.#.#... ..#.#.#.#.#.#.#.#.#.#.#.. .#.#.#.#.#.#.#.#.#.#.#.#. #.#.#.#.#.#.#.#.#.#.#.#.# ##.#.#.#.#.#.#.#.#.#.#.## .##.#.#.#.#.#.#.#.#.#.##. ####.#.#.#.#.#.#.#.#.#### ...##.#.#.#.#.#.#.#.##... ..####.#.#.#.#.#.#.####.. .##..##.#.#.#.#.#.##..##. ########.#.#.#.#.######## .......##.#.#.#.##....... ......####.#.#.####...... .....##..##.#.##..##..... ....########.########.... ...##......###......##...
ALGOL 68
BEGIN # elementary cellular automaton #
COMMENT returns the next state from state using rule s must be at least 2 characters long
and consist of # and - only
COMMENT
PROC next state = ( STRING state, INT rule )STRING:
BEGIN
COMMENT returns 1 or 0 depending on whether c = # or not COMMENT
OP TOINT = ( CHAR c )INT: IF c = "#" THEN 1 ELSE 0 FI;
# construct the state with additional extra elements to allow wrap-around #
STRING s = state[ UPB state ] + state + state[ LWB state : LWB state + 1 ];
COMMENT convert rule to a string of # or - depending on whether the bits of r are on or off
COMMENT
STRING r := "";
INT v := rule;
TO 8 DO
r +:= IF ODD v THEN "#" ELSE "-" FI;
v OVERAB 2
OD;
STRING new state := "";
FOR i FROM LWB s TO UPB s - 3 DO
CHAR c1 = s[ i ];
CHAR c2 = s[ i + 1 ];
CHAR c3 = s[ i + 2 ];
INT pos := ( ( ( TOINT c1 * 2 ) + TOINT c2 ) * 2 ) + TOINT c3;
new state +:= r[ pos + 1 ]
OD;
new state
END # next state # ;
# evolve state until the next state = the current state or 10 iterations have occured #
PROC test = ( STRING state, INT rule )VOID:
BEGIN
print( ( "Rule ", whole( rule, 0 ), newline ) );
STRING curr := state;
print( ( " 0: ", curr, newline ) );
FOR i TO 10 WHILE STRING next = next state( curr, rule );
next /= curr
DO
print( ( whole( i, -2 ), ": ", next, newline ) );
curr := next
OD
END # test # ;
# tests #
test( "---------#---------", 30 );
test( "---------#---------", 60 );
test( "---------#---------", 90 )
END- Output:
Rule 30 0: ---------#--------- 1: --------###-------- 2: -------##--#------- 3: ------##-####------ 4: -----##--#---#----- 5: ----##-####-###---- 6: ---##--#----#--#--- 7: --##-####--######-- 8: -##--#---###-----#- 9: ##-####-##--#---### 10: ---#----#-####-##-- Rule 60 0: ---------#--------- 1: ---------##-------- 2: ---------#-#------- 3: ---------####------ 4: ---------#---#----- 5: ---------##--##---- 6: ---------#-#-#-#--- 7: ---------########-- 8: ---------#-------#- 9: ---------##------## 10: #--------#-#-----#- Rule 90 0: ---------#--------- 1: --------#-#-------- 2: -------#---#------- 3: ------#-#-#-#------ 4: -----#-------#----- 5: ----#-#-----#-#---- 6: ---#---#---#---#--- 7: --#-#-#-#-#-#-#-#-- 8: -#---------------#- 9: #-#-------------#-# 10: #--#-----------#--#
AutoHotkey
state := StrSplit("0000000001000000000")
rule := 90
output := "Rule: " rule
Loop, 10 {
output .= "`n" A_Index "`t" PrintState(state)
state := NextState(state, rule)
}
Gui, Font,, Courier New
Gui, Add, Text,, % output
Gui, Show
return
GuiClose:
ExitApp
; Returns the next state based on the current state and rule.
NextState(state, rule) {
r := ByteDigits(rule)
result := {}
for i, val in state {
if (i = 1) ; The leftmost cell
result.Insert(r[state[state.MaxIndex()] state.1 state.2])
else if (i = state.MaxIndex()) ; The rightmost cell
result.Insert(r[state[i-1] val state.1])
else ; All cells between leftmost and rightmost
result.Insert(r[state[i - 1] val state[i + 1]])
}
return result
}
; Returns an array with each three digit sequence as a key corresponding to a value
; of true or false depending on the rule.
ByteDigits(rule) {
res := {}
for i, val in ["000", "001", "010", "011", "100", "101", "110", "111"] {
res[val] := Mod(rule, 2)
rule >>= 1
}
return res
}
; Converts 0 and 1 to . and # respectively and returns a string representing the state
PrintState(state) {
for i, val in state
result .= val = 1 ? "#" : "."
return result
}
- Output:
Rule: 90 1 .........#......... 2 ........#.#........ 3 .......#...#....... 4 ......#.#.#.#...... 5 .....#.......#..... 6 ....#.#.....#.#.... 7 ...#...#...#...#... 8 ..#.#.#.#.#.#.#.#.. 9 .#...............#. 10 #.#.............#.#
C
64 cells, edges are cyclic.
#include <stdio.h>
#include <limits.h>
typedef unsigned long long ull;
#define N (sizeof(ull) * CHAR_BIT)
#define B(x) (1ULL << (x))
void evolve(ull state, int rule)
{
int i;
ull st;
printf("Rule %d:\n", rule);
do {
st = state;
for (i = N; i--; ) putchar(st & B(i) ? '#' : '.');
putchar('\n');
for (state = i = 0; i < N; i++)
if (rule & B(7 & (st>>(i-1) | st<<(N+1-i))))
state |= B(i);
} while (st != state);
}
int main(int argc, char **argv)
{
evolve(B(N/2), 90);
evolve(B(N/4)|B(N - N/4), 30); // well, enjoy the fireworks
return 0;
}
- Output:
Rule 90:
................................#...............................
...............................#.#..............................
..............................#...#.............................
.............................#.#.#.#............................
............................#.......#...........................
...........................#.#.....#.#..........................
..........................#...#...#...#.........................
.........................#.#.#.#.#.#.#.#........................
........................#...............#.......................
---(output snipped)---
C#
using System;
using System.Collections;
namespace ElementaryCellularAutomaton
{
class Automata
{
BitArray cells, ncells;
const int MAX_CELLS = 19;
public void run()
{
cells = new BitArray(MAX_CELLS);
ncells = new BitArray(MAX_CELLS);
while (true)
{
Console.Clear();
Console.WriteLine("What Rule do you want to visualize");
doRule(int.Parse(Console.ReadLine()));
Console.WriteLine("Press any key to continue...");
Console.ReadKey();
}
}
private byte getCells(int index)
{
byte b;
int i1 = index - 1,
i2 = index,
i3 = index + 1;
if (i1 < 0) i1 = MAX_CELLS - 1;
if (i3 >= MAX_CELLS) i3 -= MAX_CELLS;
b = Convert.ToByte(
4 * Convert.ToByte(cells.Get(i1)) +
2 * Convert.ToByte(cells.Get(i2)) +
Convert.ToByte(cells.Get(i3)));
return b;
}
private string getBase2(int i)
{
string s = Convert.ToString(i, 2);
while (s.Length < 8)
{ s = "0" + s; }
return s;
}
private void doRule(int rule)
{
Console.Clear();
string rl = getBase2(rule);
cells.SetAll(false);
ncells.SetAll(false);
cells.Set(MAX_CELLS / 2, true);
Console.WriteLine("Rule: " + rule + "\n----------\n");
for (int gen = 0; gen < 51; gen++)
{
Console.Write("{0, 4}", gen + ": ");
foreach (bool b in cells)
Console.Write(b ? "#" : ".");
Console.WriteLine("");
int i = 0;
while (true)
{
byte b = getCells(i);
ncells[i] = '1' == rl[7 - b] ? true : false;
if (++i == MAX_CELLS) break;
}
i = 0;
foreach (bool b in ncells)
cells[i++] = b;
}
Console.WriteLine("");
}
};
class Program
{
static void Main(string[] args)
{
Automata t = new Automata();
t.run();
}
}
}
- Output:
Rule: 90 ---------- 0: .........#......... 1: ........#.#........ 2: .......#...#....... 3: ......#.#.#.#...... 4: .....#.......#..... 5: ....#.#.....#.#.... 6: ...#...#...#...#... 7: ..#.#.#.#.#.#.#.#.. 8: .#...............#. 9: #.#.............#.# 10: #..#...........#..# 11: ###.#.........#.### 12: ..#..#.......#..#.. 13: .#.##.#.....#.##.#. 14: #..##..#...#..##..# 15: #######.#.#.####### 16: ......#.....#...... 17: .....#.#...#.#..... 18: ....#...#.#...#.... 19: ...#.#.#...#.#.#... 20: ..#.....#.#.....#.. 21: .#.#...#...#...#.#. 22: #...#.#.#.#.#.#...# 23: ##.#...........#.## 24: .#..#.........#..#. 25: #.##.#.......#.##.# 26: #.##..#.....#..##.# 27: #.####.#...#.####.# 28: #.#..#..#.#..#..#.# 29: #..##.##...##.##..# 30: #####.###.###.##### 31: ....#.#.#.#.#.#.... 32: ...#...........#... 33: ..#.#.........#.#.. 34: .#...#.......#...#. 35: #.#.#.#.....#.#.#.# 36: #......#...#......# 37: ##....#.#.#.#....## 38: .##..#.......#..##. 39: #####.#.....#.##### 40: ....#..#...#..#.... 41: ...#.##.#.#.##.#... 42: ..#..##.....##..#.. 43: .#.#####...#####.#. 44: #..#...##.##...#..# 45: ###.#.###.###.#.### 46: ..#...#.#.#.#...#.. 47: .#.#.#.......#.#.#. 48: #.....#.....#.....# 49: ##...#.#...#.#...## 50: .##.#...#.#...#.##.
C++
#include <bitset>
#include <stdio.h>
#define SIZE 80
#define RULE 30
#define RULE_TEST(x) (RULE & 1 << (7 & (x)))
void evolve(std::bitset<SIZE> &s) {
int i;
std::bitset<SIZE> t(0);
t[SIZE-1] = RULE_TEST( s[0] << 2 | s[SIZE-1] << 1 | s[SIZE-2] );
t[ 0] = RULE_TEST( s[1] << 2 | s[ 0] << 1 | s[SIZE-1] );
for (i = 1; i < SIZE-1; i++)
t[i] = RULE_TEST( s[i+1] << 2 | s[i] << 1 | s[i-1] );
for (i = 0; i < SIZE; i++) s[i] = t[i];
}
void show(std::bitset<SIZE> s) {
int i;
for (i = SIZE; --i; ) printf("%c", s[i] ? '#' : ' ');
printf("\n");
}
int main() {
int i;
std::bitset<SIZE> state(1);
state <<= SIZE / 2;
for (i=0; i<10; i++) {
show(state);
evolve(state);
}
return 0;
}
- Output:
# |
### |
## # |
## #### |
## # # |
## #### ### |
## # # # |
## #### ###### |
## # ### # |
## #### ## # ### |
Ceylon
class Rule(number) satisfies Correspondence<Boolean[3], Boolean> {
shared Byte number;
"all 3 bit patterns will return a value so this is always true"
shared actual Boolean defines(Boolean[3] key) => true;
shared actual Boolean? get(Boolean[3] key) =>
number.get((key[0] then 4 else 0) + (key[1] then 2 else 0) + (key[2] then 1 else 0));
function binaryString(Integer integer, Integer maxPadding) =>
Integer.format(integer, 2).padLeading(maxPadding, '0');
string =>
let (digits = binaryString(number.unsigned, 8))
"Rule #``number``
``" | ".join { for (pattern in $111..0) binaryString(pattern, 3) }``
``" | ".join(digits.map((Character element) => element.string.pad(3)))``";
}
class ElementaryAutomaton {
shared static ElementaryAutomaton|ParseException parse(Rule rule, String cells, Character aliveChar, Character deadChar) {
if (!cells.every((Character element) => element == aliveChar || element == deadChar)) {
return ParseException("the string was not a valid automaton");
}
return ElementaryAutomaton(rule, cells.map((Character element) => element == aliveChar));
}
shared Rule rule;
Array<Boolean> cells;
shared new(Rule rule, {Boolean*} initialCells) {
this.rule = rule;
this.cells = Array { *initialCells };
}
shared Boolean evolve() {
if (cells.empty) {
return false;
}
function left(Integer index) {
assert (exists cell = cells[index - 1] else cells.last);
return cell;
}
function right(Integer index) {
assert (exists cell = cells[index + 1] else cells.first);
return cell;
}
value newCells = Array.ofSize(cells.size, false);
for (index->cell in cells.indexed) {
value neighbourhood = [left(index), cell, right(index)];
assert (exists newCell = rule[neighbourhood]);
newCells[index] = newCell;
}
if (newCells == cells) {
return false;
}
newCells.copyTo(cells);
return true;
}
shared void display(Character aliveChar = '#', Character deadChar = ' ') {
print("".join(cells.map((Boolean element) => element then aliveChar else deadChar)));
}
}
shared void run() {
value rule = Rule(90.byte);
print(rule);
value automaton = ElementaryAutomaton.parse(rule, " # ", '#', ' ');
assert (is ElementaryAutomaton automaton);
for (generation in 0..10) {
automaton.display();
automaton.evolve();
}
}
- Output:
Rule #90
111 | 110 | 101 | 100 | 011 | 010 | 001 | 000
0 | 1 | 0 | 1 | 1 | 0 | 1 | 0
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
Common Lisp
(defun automaton (init rule &optional (stop 10))
(labels ((next-gen (cells)
(mapcar #'new-cell
(cons (car (last cells)) cells)
cells
(append (cdr cells) (list (car cells)))))
(new-cell (left current right)
(let ((shift (+ (* left 4) (* current 2) right)))
(if (logtest rule (ash 1 shift)) 1 0)))
(pretty-print (cells)
(format T "~{~a~}~%"
(mapcar (lambda (x) (if (zerop x) #\. #\#))
cells))))
(loop for cells = init then (next-gen cells)
for i below stop
do (pretty-print cells))))
(automaton '(0 0 0 0 0 0 1 0 0 0 0 0 0) 90)
- Output:
......#...... .....#.#..... ....#...#.... ...#.#.#.#... ..#.......#.. .#.#.....#.#. #...#...#...# ##.#.#.#.#.## .#.........#. #.#.......#.#
D
import std.stdio, std.string, std.conv, std.range, std.algorithm, std.typecons;
enum mod = (in int n, in int m) pure nothrow @safe @nogc => ((n % m) + m) % m;
struct ECAwrap {
public string front;
public enum bool empty = false;
private immutable const(char)[string] next;
this(in string cells_, in uint rule) pure @safe {
this.front = cells_;
immutable ruleBits = "%08b".format(rule).retro.text;
next = 8.iota.map!(n => tuple("%03b".format(n), char(ruleBits[n]))).assocArray;
}
void popFront() pure @safe {
alias c = front;
c = iota(c.length)
.map!(i => next[[c[(i - 1).mod($)], c[i], c[(i + 1) % $]]])
.text;
}
}
void main() @safe {
enum nLines = 50;
immutable string start = "0000000001000000000";
immutable uint[] rules = [90, 30, 122];
writeln("Rules: ", rules);
auto ecas = rules.map!(rule => ECAwrap(start, rule)).array;
foreach (immutable i; 0 .. nLines) {
writefln("%2d: %-(%s %)", i, ecas.map!(eca => eca.front.tr("01", ".#")));
foreach (ref eca; ecas)
eca.popFront;
}
}
- Output:
Rules: [90, 30, 122] 0: .........#......... .........#......... .........#......... 1: ........#.#........ ........###........ ........#.#........ 2: .......#...#....... .......##..#....... .......#.#.#....... 3: ......#.#.#.#...... ......##.####...... ......#.#.#.#...... 4: .....#.......#..... .....##..#...#..... .....#.#.#.#.#..... 5: ....#.#.....#.#.... ....##.####.###.... ....#.#.#.#.#.#.... 6: ...#...#...#...#... ...##..#....#..#... ...#.#.#.#.#.#.#... 7: ..#.#.#.#.#.#.#.#.. ..##.####..######.. ..#.#.#.#.#.#.#.#.. 8: .#...............#. .##..#...###.....#. .#.#.#.#.#.#.#.#.#. 9: #.#.............#.# ##.####.##..#...### #.#.#.#.#.#.#.#.#.# 10: #..#...........#..# ...#....#.####.##.. ##.#.#.#.#.#.#.#.## 11: ###.#.........#.### ..###..##.#....#.#. .##.#.#.#.#.#.#.##. 12: ..#..#.......#..#.. .##..###..##..##.## ####.#.#.#.#.#.#### 13: .#.##.#.....#.##.#. .#.###..###.###..#. ...##.#.#.#.#.##... 14: #..##..#...#..##..# ##.#..###...#..#### ..####.#.#.#.####.. 15: #######.#.#.####### ...####..#.#####... .##..##.#.#.##..##. 16: ......#.....#...... ..##...###.#....#.. ########.#.######## 17: .....#.#...#.#..... .##.#.##...##..###. .......##.##....... 18: ....#...#.#...#.... ##..#.#.#.##.###..# ......#######...... 19: ...#.#.#...#.#.#... ..###.#.#.#..#..### .....##.....##..... 20: ..#.....#.#.....#.. ###...#.#.#######.. ....####...####.... 21: .#.#...#...#...#.#. #..#.##.#.#......## ...##..##.##..##... 22: #...#.#.#.#.#.#...# .###.#..#.##....##. ..###############.. 23: ##.#...........#.## ##...####.#.#..##.# .##.............##. 24: .#..#.........#..#. ..#.##....#.####..# ####...........#### 25: #.##.#.......#.##.# ###.#.#..##.#...### ...##.........##... 26: #.##..#.....#..##.# ....#.####..##.##.. ..####.......####.. 27: #.####.#...#.####.# ...##.#...###..#.#. .##..##.....##..##. 28: #.#..#..#.#..#..#.# ..##..##.##..###.## ########...######## 29: #..##.##...##.##..# ###.###..#.###...#. .......##.##....... 30: #####.###.###.##### #...#..###.#..#.##. ......#######...... 31: ....#.#.#.#.#.#.... ##.#####...####.#.. .....##.....##..... 32: ...#...........#... #..#....#.##....### ....####...####.... 33: ..#.#.........#.#.. .####..##.#.#..##.. ...##..##.##..##... 34: .#...#.......#...#. ##...###..#.####.#. ..###############.. 35: #.#.#.#.....#.#.#.# #.#.##..###.#....#. .##.............##. 36: #......#...#......# #.#.#.###...##..##. ####...........#### 37: ##....#.#.#.#....## #.#.#.#..#.##.###.. ...##.........##... 38: .##..#.......#..##. #.#.#.####.#..#..## ..####.......####.. 39: #####.#.....#.##### ..#.#.#....#######. .##..##.....##..##. 40: ....#..#...#..#.... .##.#.##..##......# ########...######## 41: ...#.##.#.#.##.#... .#..#.#.###.#....## .......##.##....... 42: ..#..##.....##..#.. .####.#.#...##..##. ......#######...... 43: .#.#####...#####.#. ##....#.##.##.###.# .....##.....##..... 44: #..#...##.##...#..# ..#..##.#..#..#...# ....####...####.... 45: ###.#.###.###.#.### ######..########.## ...##..##.##..##... 46: ..#...#.#.#.#...#.. ......###........#. ..###############.. 47: .#.#.#.......#.#.#. .....##..#......### .##.............##. 48: #.....#.....#.....# #...##.####....##.. ####...........#### 49: ##...#.#...#.#...## ##.##..#...#..##.## ...##.........##...
EasyLang
global celln[] cell[] .
len map[] 8
#
proc evolve . .
for i = 1 to len cell[]
ind = 0
for j = i + 1 downto i - 1
ind = ind * 2 + cell[j mod1 len cell[]]
.
celln[i] = map[ind + 1]
.
swap celln[] cell[]
.
proc show . .
c$[] = [ "." "#" ]
for v in cell[]
write c$[v + 1]
.
print ""
.
proc run map count inp[] . .
for i to 8
map[i] = map mod 2
map = map div 2
.
swap cell[] inp[]
len celln[] len cell[]
show
for i to count
evolve
show
.
print ""
.
run 104 9 [ 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 ]
run 90 9 [ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ]
run 122 15 [ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ]- Output:
.###.##.#.#.#.#..#.. .#.#####.#.#.#...... ..##...##.#.#....... ..##...###.#........ ..##...#.##......... ..##....###......... ..##....#.#......... ..##.....#.......... ..##................ ..##................ .......#....... ......#.#...... .....#...#..... ....#.#.#.#.... ...#.......#... ..#.#.....#.#.. .#...#...#...#. #.#.#.#.#.#.#.# #.............# ##...........## .......#....... ......#.#...... .....#.#.#..... ....#.#.#.#.... ...#.#.#.#.#... ..#.#.#.#.#.#.. .#.#.#.#.#.#.#. #.#.#.#.#.#.#.# ##.#.#.#.#.#.## .##.#.#.#.#.##. ####.#.#.#.#### ...##.#.#.##... ..####.#.####.. .##..##.##..##. ############### ...............
EchoLisp
Pictures of the (nice) generated colored bit-maps : The Escher like (task 90 5) and the fractal like (task 22 1)
(lib 'types) ;; int32 vectors
(lib 'plot)
(define-constant BIT0 0)
(define-constant BIT1 (rgb 0.8 0.9 0.7)) ;; colored bit 1
;; integer to pattern
(define ( n->pat n)
(for/vector ((i 8))
#:when (bitwise-bit-set? n i)
(for/vector ((j (in-range 2 -1 -1)))
(if (bitwise-bit-set? i j) BIT1 BIT0 ))))
;; test if three pixels match a pattern
(define (pmatch a b c pat)
(for/or ((v pat))
(and (= a (vector-ref v 0)) (= b (vector-ref v 1)) (= c (vector-ref v 2)) )))
;; next generation = next row
(define (generate x0 width PAT PIX (x))
(for ((dx (in-range 0 width)))
(set! x (+ x0 dx))
(vector-set! PIX (+ x width) ;; next row
(if
(pmatch
(vector-ref PIX (if (zero? dx) (+ x0 width) (1- x))) ;; let's wrap
(vector-ref PIX x)
(vector-ref PIX (if (= dx (1- width)) x0 (1+ x)))
PAT)
BIT1 BIT0))))
;; n is the pattern, starters in the number of set pixels at generation 0
(define (task n (starters 1))
(define width (first (plot-size)))
(define height (rest (plot-size)))
(define PAT (n->pat n))
(plot-clear)
(define PIX (pixels->int32-vector))
(init-pix starters width height PIX)
(for ((y (1- height)))
(generate (* y width) width PAT into: PIX))
(vector->pixels PIX))
;; put n starters on first row
(define (init-pix starters width height PIX)
(define dw (floor (/ width (1+ starters))))
(for ((x (in-range dw width (1+ dw))))
(vector-set! PIX x BIT1)))
;; usage
(task 99 3) → 672400 ;; ESC to see it
(task 22) → 672400
;; check pattern generator
(n->pat 13)
→ #( #( 0 0 0) #( 0 -5052980 0) #( 0 -5052980 -5052980))
Elixir
defmodule Elementary_cellular_automaton do
def run(start_str, rule, times) do
IO.puts "rule : #{rule}"
each(start_str, rule_pattern(rule), times)
end
defp rule_pattern(rule) do
list = Integer.to_string(rule, 2) |> String.pad_leading(8, "0")
|> String.codepoints |> Enum.reverse
Enum.map(0..7, fn i -> Integer.to_string(i, 2) |> String.pad_leading(3, "0") end)
|> Enum.zip(list) |> Map.new
end
defp each(_, _, 0), do: :ok
defp each(str, patterns, times) do
IO.puts String.replace(str, "0", ".") |> String.replace("1", "#")
str2 = String.last(str) <> str <> String.first(str)
next_str = Enum.map_join(0..String.length(str)-1, fn i ->
Map.get(patterns, String.slice(str2, i, 3))
end)
each(next_str, patterns, times-1)
end
end
pad = String.duplicate("0", 14)
str = pad <> "1" <> pad
Elementary_cellular_automaton.run(str, 18, 25)
- Output:
rule : 18 ..............#.............. .............#.#............. ............#...#............ ...........#.#.#.#........... ..........#.......#.......... .........#.#.....#.#......... ........#...#...#...#........ .......#.#.#.#.#.#.#.#....... ......#...............#...... .....#.#.............#.#..... ....#...#...........#...#.... ...#.#.#.#.........#.#.#.#... ..#.......#.......#.......#.. .#.#.....#.#.....#.#.....#.#. #...#...#...#...#...#...#...# .#.#.#.#.#.#.#.#.#.#.#.#.#.#. #...........................# .#.........................#. #.#.......................#.# ...#.....................#... ..#.#...................#.#.. .#...#.................#...#. #.#.#.#...............#.#.#.# .......#.............#....... ......#.#...........#.#......
F#
The Function
// Elementary Cellular Automaton . Nigel Galloway: July 31st., 2019
let eca N=
let N=Array.init 8 (fun n->(N>>>n)%2)
Seq.unfold(fun G->Some(G,[|yield Array.last G; yield! G; yield Array.head G|]|>Array.windowed 3|>Array.map(fun n->N.[n.[2]+2*n.[1]+4*n.[0]])))
The Task
eca 90 [|0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;1;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0|] |> Seq.take 80 |> Seq.iter(fun n->Array.iter(fun n->printf "%s" (if n=0 then " " else "@"))n; printfn "")
- Output:
@
@ @
@ @
@ @ @ @
@ @
@ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @
@ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @
@ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @
@@ @@
@@ @@
@@@@ @@@@
@@ @@
@@@@ @@@@
@@ @@ @@ @@
@@@@@@@@ @@@@@@@@
@@ @@
@@@@ @@@@
@@ @@ @@ @@
@@@@@@@@ @@@@@@@@
@@ @@ @@ @@
@@@@ @@@@ @@@@ @@@@
@@ @@ @@ @@ @@ @@ @@ @@
@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@
@@ @@
@@@@ @@@@
@@ @@ @@ @@
@@@@@@@@ @@@@@@@@
@@ @@ @@ @@
@@@@ @@@@ @@@@ @@@@
@@ @@ @@ @@ @@ @@ @@ @@
@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@
@@ @@ @@ @@
@@@@ @@@@ @@@@ @@@@
@@ @@ @@ @@ @@ @@ @@ @@
@@@@@@@@ @@@@@@@@ @@@@@@@@ @@@@@@@@
@@ @@ @@ @@ @@ @@ @@ @@
@@@@ @@@@ @@@@ @@@@ @@@@ @@@@ @@@@ @@@@
@@ @@ @@ @@ @@ @@ @@ @@ @@ @@ @@ @@ @@ @@ @@ @@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@ @
@ @
@ @ @ @
@ @
@ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @
@ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @
eca 110 [|0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;1|] |> Seq.take 80 |> Seq.iter(fun n->Array.iter(fun n->printf "%s" (if n=0 then " " else "@"))n; printfn "")
- Output:
@
@@
@@@
@@ @
@@@@@
@@ @
@@@ @@
@@ @ @@@
@@@@@@@ @
@@ @@@
@@@ @@ @
@@ @ @@@@@
@@@@@ @@ @
@@ @ @@@ @@
@@@ @@@@ @ @@@
@@ @ @@ @@@@@ @
@@@@@@@@ @@ @@@
@@ @@@@ @@ @
@@@ @@ @ @@@@@
@@ @ @@@ @@@@ @
@@@@@ @@ @@@ @ @@
@@ @ @@@@@ @ @@ @@@
@@@ @@ @@ @@@@@@@@ @
@@ @ @@@@@@ @@ @@@
@@@@@@@ @ @@@ @@ @
@@ @ @@@@ @ @@@@@
@@@ @@ @@ @@@ @@ @
@@ @ @@@ @@@ @@ @ @@@ @@
@@@@@ @@ @@@ @@@@@@ @@ @ @@@
@@ @ @@@@@ @@@ @@@@@@@@ @
@@@ @@@@ @@@ @ @@ @@@
@@ @ @@ @ @@ @@@ @@@ @@ @
@@@@@@@@ @@ @@@@@ @ @@ @ @@@@@
@@ @@@@@@ @@@@@@@@ @@ @
@@@ @@ @ @@ @ @@@ @@
@@ @ @@@ @@ @@@ @@ @@ @ @@@
@@@@@ @@ @ @@@@@ @ @@@@@@@@@@ @
@@ @ @@@@@ @@ @@@ @@ @@@
@@@ @@ @@ @@@@ @@ @ @@@ @@ @
@@ @ @@@@@@ @@ @ @@@@@ @@ @ @@@@@
@@@@@@@ @ @@@ @@@@ @@@@@@ @@ @
@@ @ @@@@ @@@ @ @@ @ @@@ @@
@@@ @@ @@ @@@ @ @@ @@@ @@ @@ @ @@@
@@ @ @@@ @@@ @@ @@@@@@@@ @ @@@ @@@@@@@ @
@@@@@ @@ @@@ @@@@@@ @@@ @@ @ @@ @@@
@@ @ @@@@@ @@@ @ @@ @@@@@@@@@ @@ @
@@@ @@@@ @@@ @ @@ @@@@@ @ @@@@@
@@ @ @@ @ @@ @@@ @@@ @@ @ @@ @@ @
@@@@@@@@ @@ @@@@@ @ @@ @ @@@ @@ @@@ @@@ @@
@@ @@@@@@ @@@@@@@@ @@ @ @@@ @@ @@@ @ @@@
@@@ @@ @ @@ @@@@@@@@ @ @@@@@ @@@@@ @
@@ @ @@@ @@ @@@ @@ @@@ @@ @@@ @@@
@@@@@ @@ @ @@@@@ @ @@@ @@ @ @@@ @@ @ @@ @
@@ @ @@@@@ @@ @@@ @@ @ @@@@@@@ @ @@@@@ @@@@@
@@@ @@ @@ @@@@ @@ @ @@@@@ @@ @@@@@ @@@ @
@@ @ @@@@@@ @@ @ @@@@@ @@ @ @@@ @@ @ @@ @ @@
@@@@@@@ @ @@@ @@@@ @@@@ @@ @@ @ @@@ @@ @@@@@ @@@
@@ @ @@@@ @@@ @ @@ @ @@@@@@@@ @@ @ @@@@@ @@@ @
@@@ @@ @@ @@@ @ @@ @@@ @@@@ @ @@@@@@@ @ @@ @@@
@@ @ @@@ @@@ @@ @@@@@@@@ @@@ @ @@@@ @ @@ @@@@@ @
@@@@@ @@ @@@ @@@@@@ @@@ @ @@ @@ @ @@ @@@@@ @@@
@@ @ @@@@@ @@@ @ @@ @@@@@@ @@@ @@ @@@@@ @ @@ @
@@@ @@@@ @@@ @ @@ @@@@@ @ @@ @@@@ @@ @ @@ @@@@@
@@ @ @@ @ @@ @@@ @@@ @@ @ @@ @@@@@ @ @@@ @@ @@@@@ @
@@@@@@@@ @@ @@@@@ @ @@ @ @@@ @@ @@@@@ @ @@@@ @ @@@@@ @ @@
@@@@@@ @@@@@@@@ @@ @ @@@ @@ @ @@@@ @@@@@ @ @@ @@
@@ @ @@ @@@@@@@@ @@@@ @@ @@ @ @@ @ @@ @@@@@@
@@@ @@ @@@ @@ @@@ @ @@@@@@ @@@@@ @@ @@@@@ @
@@ @ @@@@@ @ @@@ @@ @ @@@@ @@@ @ @@@@@ @ @@
@@@@@ @@ @@@ @@ @ @@@@@@@ @ @@ @ @@@@ @ @@ @@@
@@ @@@@ @@ @ @@@@@ @@ @ @@ @@@@@ @@ @ @@ @@@ @@ @
@@@ @@ @ @@@@@ @@ @ @@@ @@@@@ @@ @@@@ @@ @@@@@ @@@@@@
@@ @ @@@ @@@@ @@@@ @@ @@ @ @@ @@@@ @@ @@@@@@ @@@ @
@@@@@@ @@@ @ @@ @ @@@@@@@@ @@@ @@ @ @@@ @@ @ @@ @ @@@
@@@ @ @@ @@@ @@@@ @ @@ @ @@@ @@@@ @@@@ @@ @@@@@ @@
@@ @@@@@@@@ @@@ @ @@@@@@@@@ @@@ @@@ @ @@@@@ @ @@@
@@@@@ @@@ @ @@ @@ @@@ @ @@ @ @@ @@ @ @@@@ @
@@ @ @@ @@@@@@ @@@ @@ @@@@@@@@@@@@@@ @@ @@ @@@
@@@ @@ @@@@@ @ @@ @ @@@@@ @ @@@@@@ @@ @
@@ @ @@@ @@ @ @@ @@@@@ @@ @ @@@@ @@@@@@
Factor
USING: assocs formatting grouping io kernel math math.bits
math.combinatorics sequences sequences.extras ;
: make-rules ( n -- assoc )
{ f t } 3 selections swap make-bits 8 f pad-tail zip ;
: next-state ( assoc seq -- assoc seq' )
dupd 3 circular-clump -1 rotate [ of ] with map ;
: first-state ( -- seq ) 15 f <repetition> dup { t } glue ;
: show-state ( seq -- ) [ "#" "." ? write ] each nl ;
: show-automaton ( rule -- )
dup "Rule %d:\n" printf make-rules first-state 16
[ dup show-state next-state ] times 2drop ;
90 show-automaton
- Output:
Rule 90: ...............#............... ..............#.#.............. .............#...#............. ............#.#.#.#............ ...........#.......#........... ..........#.#.....#.#.......... .........#...#...#...#......... ........#.#.#.#.#.#.#.#........ .......#...............#....... ......#.#.............#.#...... .....#...#...........#...#..... ....#.#.#.#.........#.#.#.#.... ...#.......#.......#.......#... ..#.#.....#.#.....#.#.....#.#.. .#...#...#...#...#...#...#...#. #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
Forth
#! /usr/bin/gforth
\ Elementary cellular automaton
\ checks if bit ix (where 0 is the least significant one) of u is set
: bit? ( u ix -- f )
1 over lshift rot and swap rshift 1 =
;
\ displays a bit-array with n bits starting at address addr
: .arr ( addr n -- )
0 DO
dup @ IF 1 ELSE 0 THEN .
cell +
LOOP
drop
;
\ applies rule r to the bit-array with n bits starting at address addr
: generation { r addr n -- }
addr n 1- cells + @ IF 2 ELSE 0 THEN
addr @ tuck IF 1 ELSE 0 THEN
+
n 0 ?DO
i n 1- = IF swap ELSE addr i 1+ cells + @ THEN
IF 1 ELSE 0 THEN
swap 1 lshift +
r over bit?
addr i cells + !
3 and
LOOP
drop
;
\ evolves a rule over several generations
: evolve { r addr n m -- }
." P1" cr
n . m . cr
addr n .arr cr
m 1- 0 ?DO
r addr n generation
addr n .arr cr
LOOP
;
\ evolves a rule over several generations and saves the result as a pbm-image
\ and writes the result to file c-addr u
: evolve-pbm ( r addr n m c-addr u -- )
w/o create-file throw dup 2>r
['] evolve r> outfile-execute
r> close-file throw
;
CREATE arr 1000 cells allot
arr 1000 cells erase
true arr 500 cells + !
30 arr 1000 2000 s" rule-030.pbm" evolve-pbm
arr 1000 cells erase
true arr 500 cells + !
60 arr 1000 2000 s" rule-060.pbm" evolve-pbm
arr 1000 cells erase
true arr 500 cells + !
90 arr 1000 2000 s" rule-090.pbm" evolve-pbm
arr 1000 cells erase
true arr 500 cells + !
110 arr 1000 2000 s" rule-110.pbm" evolve-pbm
bye
- Output:
starting with 1000 cells, where all but one in the middle are initially empty, evolving over 2000 generations:
![[1]](https://commons.wikimedia.org/wiki/File:Rule-030.png){kind=link}
![[2]](https://commons.wikimedia.org/wiki/File:Rule-060.png){kind=link}
![[3]](https://commons.wikimedia.org/wiki/File:Rule-090.png){kind=link}
![[4]](https://commons.wikimedia.org/wiki/File:Rule-110.png){kind=link}
FreeBASIC
#define NCELLS 400
#define border 16
dim as ubyte rule = 110
sub evolve( row as uinteger, rule as ubyte, pattern() as ubyte )
dim as ubyte newp(NCELLS)
dim as uinteger i
dim as ubyte lookup
for i = 0 to NCELLS-1
pset (i + border, row + border ), pattern(i)*15
lookup = 4*pattern((i-1) mod NCELLS) + 2*pattern(i) + pattern( (i+1) mod NCELLS )
newp(i)=0
if ( 2^lookup and rule )<>0 then newp(i) = 1
next i
for i = 0 to NCELLS-1
pattern(i) = newp(i)
next i
end sub
sub perform_simulation( rule as ubyte, pattern() as ubyte )
dim as integer i
for i = 1 to NCELLS
evolve(i, rule, pattern())
next i
end sub
sub reseed( pattern() as ubyte )
dim as integer i
for i = 0 to NCELLS-1
pattern(i) = int(rnd+0.5)
next i
end sub
sub display_text( rule as ubyte )
locate 4,58 : print using "Rule ###";rule
locate 6,53 : print " R: reshuffle seed "
locate 8,53 : print " <,>: change rule "
locate 10,53 : print " Q: quit "
end sub
screen 12
randomize timer
dim as boolean pattern(0 to NCELLS-1)
dim as string key="R"
do
if key = "R" then
cls
reseed(pattern())
perform_simulation(rule,pattern())
display_text(rule)
end if
if key="<" then
cls
rule = (rule-1) mod 256
reseed(pattern())
perform_simulation(rule,pattern())
display_text(rule)
end if
if key=">" then
cls
rule = (rule+1) mod 256
reseed(pattern())
perform_simulation(rule,pattern())
display_text(rule)
end if
key = ucase(inkey)
loop until ucase(key) = "Q"
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
Test case. Generating all the 256 values:
Furor
argc 4 < { ."Usage: " 0 argv sprint SPACE 1 argv sprint SPACE ."rule size\n"
."The \"rule\" and \"size\" are numbers.\n"
."0<=rule<=255\n" end }
zero gen
3 argv #s (#g) sto maxcell
2 argv (#g) sto rule
#g argc 5 >= { 4 argv #s (#g) sto gen }
@maxcell mem !maximize sto livingspace
@maxcell mem sto originallivingspace
@maxcell {| @livingspace {} 0 [^] |} @livingspace @maxcell #g 2 / 1 [^]
infi: {...
originallivingspace @livingspace #s =
@livingspace {~ #k @@ { '* }{ '. } print |} NL
#g
@livingspace~ lsp: {|
zero a
@originallivingspace {} ? @maxcell -- [] { 4 sto a }
@originallivingspace {} [] { @a 2 | sto a }
@originallivingspace {+} @maxcell == { 0 }{ {+} } [] { @a 1 | sto a }
8 {| @rule 1 {} << & {
{} @a == { @livingspace {}§lsp 1 [^] {<}§lsp }
}
|}
z: @livingspace {} 0 [^] {<}
|}
#s @originallivingspace @livingspace == { {.>.} }
@gen { {...} @gen #g == { {.>.} } }
...}
."Generations: " {...}§infi #g printnl
@livingspace free
@originallivingspace free
end
{ „maxcell” }
{ „rule” }
{ „state” }
{ „livingspace” }
{ „originallivingspace” }
{ „a” }
{ „gen” }
// =================================================- Output:
furor eca.upu 90 100 33 ..................................................*................................................. .................................................*.*................................................ ................................................*...*............................................... ...............................................*.*.*.*.............................................. ..............................................*.......*............................................. .............................................*.*.....*.*............................................ ............................................*...*...*...*........................................... ...........................................*.*.*.*.*.*.*.*.......................................... ..........................................*...............*......................................... .........................................*.*.............*.*........................................ ........................................*...*...........*...*....................................... .......................................*.*.*.*.........*.*.*.*...................................... ......................................*.......*.......*.......*..................................... .....................................*.*.....*.*.....*.*.....*.*.................................... ....................................*...*...*...*...*...*...*...*................................... ...................................*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.................................. ..................................*...............................*................................. .................................*.*.............................*.*................................ ................................*...*...........................*...*............................... ...............................*.*.*.*.........................*.*.*.*.............................. ..............................*.......*.......................*.......*............................. .............................*.*.....*.*.....................*.*.....*.*............................ ............................*...*...*...*...................*...*...*...*........................... ...........................*.*.*.*.*.*.*.*.................*.*.*.*.*.*.*.*.......................... ..........................*...............*...............*...............*......................... .........................*.*.............*.*.............*.*.............*.*........................ ........................*...*...........*...*...........*...*...........*...*....................... .......................*.*.*.*.........*.*.*.*.........*.*.*.*.........*.*.*.*...................... ......................*.......*.......*.......*.......*.......*.......*.......*..................... .....................*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.................... ....................*...*...*...*...*...*...*...*...*...*...*...*...*...*...*...*................... ...................*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.................. ..................*...............................................................*................. .................*.*.............................................................*.*................ Generations: 33
Peri
###sysinclude standard.uh
###sysinclude system.uh
###sysinclude args.uh
###sysinclude str.uh
#g argc 4 < { ."Usage: " 0 argv sprint SPACE 1 argv sprint SPACE ."rule size\n"
."The \"rule\" and \"size\" are numbers.\n"
."0<=rule<=255\n" end }
terminallines 3 - sto gen
3 argv #s (#g) sto maxcell
2 argv (#g) sto rule
#g argc 5 >= { 4 argv #s (#g) sto gen }
@maxcell mem !maximize sto livingspace
@maxcell mem sto originallivingspace
@maxcell {{ @livingspace {{}} 0 inv [] }} @livingspace @maxcell #g 2 / 1 inv []
{..
originallivingspace @livingspace #s =
livingspace {~ #k {~?~} { '* }{ '. } print ~} NL
#g
livingspace~ lsp: {{
zero aa
@originallivingspace {{}} ? @maxcell -- [] { 4 sto aa }
@originallivingspace {{}} [] { @aa 2 | sto aa }
@originallivingspace {{+}} @maxcell == { 0 }{ {{+}} } [] { @aa 1 | sto aa }
8 {{ @rule 1 {{}} << & {
{{}} @aa == { @livingspace {{}}§lsp 1 inv [] {{<}}§lsp }
}
}}
z: @livingspace {{}} 0 inv [] {{<}}
}}
#s @originallivingspace @livingspace == { {.>.} }
@gen { {..} @gen #g == { {.>.} } }
{..} sto l
..}
."Generations: " l #g printnl
@livingspace inv mem
@originallivingspace inv mem
end
{ „maxcell” }
{ „rule” }
{ „state” }
{ „livingspace” }
{ „originallivingspace” }
{ „aa” }
{ „gen” }
// ===============================================================================- Output:
peri eca.upu 90 100 33 ..................................................*................................................. .................................................*.*................................................ ................................................*...*............................................... ...............................................*.*.*.*.............................................. ..............................................*.......*............................................. .............................................*.*.....*.*............................................ ............................................*...*...*...*........................................... ...........................................*.*.*.*.*.*.*.*.......................................... ..........................................*...............*......................................... .........................................*.*.............*.*........................................ ........................................*...*...........*...*....................................... .......................................*.*.*.*.........*.*.*.*...................................... ......................................*.......*.......*.......*..................................... .....................................*.*.....*.*.....*.*.....*.*.................................... ....................................*...*...*...*...*...*...*...*................................... ...................................*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.................................. ..................................*...............................*................................. .................................*.*.............................*.*................................ ................................*...*...........................*...*............................... ...............................*.*.*.*.........................*.*.*.*.............................. ..............................*.......*.......................*.......*............................. .............................*.*.....*.*.....................*.*.....*.*............................ ............................*...*...*...*...................*...*...*...*........................... ...........................*.*.*.*.*.*.*.*.................*.*.*.*.*.*.*.*.......................... ..........................*...............*...............*...............*......................... .........................*.*.............*.*.............*.*.............*.*........................ ........................*...*...........*...*...........*...*...........*...*....................... .......................*.*.*.*.........*.*.*.*.........*.*.*.*.........*.*.*.*...................... ......................*.......*.......*.......*.......*.......*.......*.......*..................... .....................*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.................... ....................*...*...*...*...*...*...*...*...*...*...*...*...*...*...*...*................... ...................*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.................. ..................*...............................................................*................. .................*.*.............................................................*.*................ Generations: 33
GFA Basic
'
' Elementary One-Dimensional Cellular Automaton
'
' World is cyclic, and rules are defined by a parameter
'
' start$="01110110101010100100" ! start state for world
' rules%=104 ! number defining rule-set to use
start$="00000000000000000000100000000000000000000"
rules%=18
max_cycles%=20 ! give a maximum depth to world
'
' Global variables hold the world, with two rows
' world! is treated as cyclical
' cur% gives the row for current world,
' new% gives the row for the next world.
'
size%=LEN(start$)
DIM world!(size%,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%-1,0)=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%-1,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%-1,new%)=@new_state(@get_value(i%-1))
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%-1,cur%)<>world!(i%-1,new%)
RETURN FALSE
ENDIF
NEXT i%
RETURN TRUE
ENDFUNC
'
' Return new state of cell given value
'
FUNCTION new_state(value%)
RETURN BTST(rules%,value%)
ENDFUNC
'
' Compute value for cell + neighbours
'
FUNCTION get_value(cell%)
LOCAL result%
result%=0
IF cell%-1<0 ! check for wrapping at left
IF world!(size%-1,cur%)
result%=result%+4
ENDIF
ELSE ! no wrapping
IF world!(cell%-1,cur%)
result%=result%+4
ENDIF
ENDIF
IF world!(cell%,cur%)
result%=result%+2
ENDIF
IF cell%+1>size% ! check for wrapping at right
IF world!(0,cur%)
result%=result%+1
ENDIF
ELSE ! no wrapping
IF world!(cell%+1,cur%)
result%=result%+1
ENDIF
ENDIF
RETURN result%
ENDFUNC
Go
package main
import (
"fmt"
"math/big"
"math/rand"
"strings"
)
func main() {
const cells = 20
const generations = 9
fmt.Println("Single 1, rule 90:")
a := big.NewInt(1)
a.Lsh(a, cells/2)
elem(90, cells, generations, a)
fmt.Println("Random intial state, rule 30:")
a = big.NewInt(1)
a.Rand(rand.New(rand.NewSource(3)), a.Lsh(a, cells))
elem(30, cells, generations, a)
}
func elem(rule uint, cells, generations int, a *big.Int) {
output := func() {
fmt.Println(strings.Replace(strings.Replace(
fmt.Sprintf("%0*b", cells, a), "0", " ", -1), "1", "#", -1))
}
output()
a1 := new(big.Int)
set := func(cell int, k uint) {
a1.SetBit(a1, cell, rule>>k&1)
}
last := cells - 1
for r := 0; r < generations; r++ {
k := a.Bit(last) | a.Bit(0)<<1 | a.Bit(1)<<2
set(0, k)
for c := 1; c < last; c++ {
k = k>>1 | a.Bit(c+1)<<2
set(c, k)
}
set(last, k>>1|a.Bit(0)<<2)
a, a1 = a1, a
output()
}
}
- Output:
Single 1, rule 90:
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
Random intial state, rule 30:
# # # #### #
## ## #### # ##
# # # # ### ##
######### ## # # #
# ## ## #
# ##### # #
# ## ######
## ## # ##
## # ## #### #
# #### ### ## #
Haskell
Array-based solution
Straight-forward implementation of CA on a cyclic domain, using immutable arrays:
import Data.Array (listArray, (!), bounds, elems)
step rule a = listArray (l,r) res
where (l,r) = bounds a
res = [rule (a!r) (a!l) (a!(l+1)) ] ++
[rule (a!(i-1)) (a!i) (a!(i+1)) | i <- [l+1..r-1] ] ++
[rule (a!(r-1)) (a!r) (a!l) ]
runCA rule = iterate (step rule)
The following gives decoding of the CA rule and prepares the initial CA state:
rule n l x r = n `div` (2^(4*l + 2*x + r)) `mod` 2
initial n = listArray (0,n-1) . center . padRight n
where
padRight n lst = take n $ lst ++ repeat 0
center = take n . drop (n `div` 2+1) . cycle
Finally the IO stuff:
displayCA n rule init = mapM_ putStrLn $ take n result
where result = fmap display . elems <$> runCA rule init
display 0 = ' '
display 1 = '*'
- Output:
λ> displayCA 40 (rule 90) (initial 40 [1])
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Comonadic solution
This solution is more involved, but it is slightly more efficient than Array-based one. What is more important, this solution is guaranteed to be total and correct by type checker.
The cyclic CA domain is represented by an infinite zipper list. First we provide the datatype, the viewer and constructor:
{-# LANGUAGE DeriveFunctor #-}
import Control.Comonad
import Data.InfList (InfList (..))
import qualified Data.InfList as Inf
data Cycle a = Cycle Int a a (InfList a) deriving Functor
view (Cycle n _ x r) = Inf.take n (x ::: r)
fromList [] = let a = a in Cycle 0 a a (Inf.repeat a)
-- zero cycle length ensures that elements of the empty cycle will never be accessed
fromList lst = let x:::r = Inf.cycle lst
in Cycle (length lst) (last lst) x r
In order to run the CA on the domain we make it an instance of Comonad class. Running the CA turns to be just an iterative comonadic extension of the rule:
instance Comonad Cycle where
extract (Cycle _ _ x _) = x
duplicate x@(Cycle n _ _ _) = fromList $ take n $ iterate shift x
where shift (Cycle n _ x (r:::rs)) = Cycle n x r rs
step rule (Cycle _ l x (r:::_)) = rule l x r
runCA rule = iterate (=>> step rule)
Rule definition and I/O routine is the same as in Array-based solution:
rule n l x r = n `div` (2^(4*l + 2*x + r)) `mod` 2
initial n lst = fromList $ center $ padRight n lst
where
padRight n lst = take n $ lst ++ repeat 0
center = take n . drop (n `div` 2+1) . cycle
displayCA n rule init = mapM_ putStrLn $ take n result
where result = fmap display . view <$> runCA rule init
display 0 = ' '
display 1 = '*'
See also Elementary cellular automaton/Infinite length#Haskell
J
We'll define a state transition mechanism, and then rely on the language for iteration and display:
next=: ((8$2) #: [) {~ 2 #. 1 - [: |: |.~"1 0&_1 0 1@]
' *'{~90 next^:(i.9) 0 0 0 0 0 0 1 0 0 0 0 0
*
* *
* *
* * * *
* *
* * * *
* *
* * * *
* *
Or, we can view this on a larger scale, graphically:
require'viewmat'
viewmat 90 next^:(i.200) 0=i:200
Java
import java.awt.*;
import java.awt.event.ActionEvent;
import javax.swing.*;
import javax.swing.Timer;
public class WolframCA extends JPanel {
final int[] ruleSet = {30, 45, 50, 57, 62, 70, 73, 75, 86, 89, 90, 99,
101, 105, 109, 110, 124, 129, 133, 135, 137, 139, 141, 164,170, 232};
byte[][] cells;
int rule = 0;
public WolframCA() {
Dimension dim = new Dimension(900, 450);
setPreferredSize(dim);
setBackground(Color.white);
setFont(new Font("SansSerif", Font.BOLD, 28));
cells = new byte[dim.height][dim.width];
cells[0][dim.width / 2] = 1;
new Timer(5000, (ActionEvent e) -> {
rule++;
if (rule == ruleSet.length)
rule = 0;
repaint();
}).start();
}
private byte rules(int lhs, int mid, int rhs) {
int idx = (lhs << 2 | mid << 1 | rhs);
return (byte) (ruleSet[rule] >> idx & 1);
}
void drawCa(Graphics2D g) {
g.setColor(Color.black);
for (int r = 0; r < cells.length - 1; r++) {
for (int c = 1; c < cells[r].length - 1; c++) {
byte lhs = cells[r][c - 1];
byte mid = cells[r][c];
byte rhs = cells[r][c + 1];
cells[r + 1][c] = rules(lhs, mid, rhs); // next generation
if (cells[r][c] == 1) {
g.fillRect(c, r, 1, 1);
}
}
}
}
void drawLegend(Graphics2D g) {
String s = String.valueOf(ruleSet[rule]);
int sw = g.getFontMetrics().stringWidth(s);
g.setColor(Color.white);
g.fillRect(16, 5, 55, 30);
g.setColor(Color.darkGray);
g.drawString(s, 16 + (55 - sw) / 2, 30);
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
drawCa(g);
drawLegend(g);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Wolfram CA");
f.setResizable(false);
f.add(new WolframCA(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}
JavaScript
const alive = '#';
const dead = '.';
// ------------------------------------------------------------[ Bit banging ]--
const setBitAt = (val, idx) => BigInt(val) | (1n << BigInt(idx));
const clearBitAt = (val, idx) => BigInt(val) & ~(1n << BigInt(idx));
const getBitAt = val => idx => (BigInt(val) >> BigInt(idx)) & 1n;
const hasBitAt = val => idx => ((BigInt(val) >> BigInt(idx)) & 1n) === 1n;
// ----------------------------------------------------------------[ Utility ]--
const makeArr = n => Array(n).fill(0);
const reverse = x => Array.from(x).reduce((p, c) => [c, ...p], []);
const numToLine = width => int => {
const test = hasBitAt(int);
const looper = makeArr(width);
return reverse(looper.map((_, i) => test(i) ? alive : dead)).join('');
}
// -------------------------------------------------------------------[ Main ]--
const displayCA = (rule, width, lines, startIndex) => {
const result = [];
result.push(`Rule:${rule} Width:${width} Gen:${lines}\n`)
const ruleTest = hasBitAt(rule);
const lineLoop = makeArr(lines);
const looper = makeArr(width);
const pLine = numToLine(width);
let nTarget = setBitAt(0n, startIndex);
result.push(pLine(nTarget));
lineLoop.forEach(() => {
const bitTest = getBitAt(nTarget);
looper.forEach((e, i) => {
const l = bitTest(i === 0 ? width - 1 : i - 1);
const m = bitTest(i);
const r = bitTest(i === width - 1 ? 0 : i + 1);
nTarget = ruleTest(
parseInt([l, m, r].join(''), 2))
? setBitAt(nTarget, i)
: clearBitAt(nTarget, i);
});
result.push(pLine(nTarget));
});
return result.join('\n');
}
displayCA(90, 57, 31, 28);
- Output:
Rule:90 Width:57 Gen:31 ............................#............................ ...........................#.#........................... ..........................#...#.......................... .........................#.#.#.#......................... ........................#.......#........................ .......................#.#.....#.#....................... ......................#...#...#...#...................... .....................#.#.#.#.#.#.#.#..................... ....................#...............#.................... ...................#.#.............#.#................... ..................#...#...........#...#.................. .................#.#.#.#.........#.#.#.#................. ................#.......#.......#.......#................ ...............#.#.....#.#.....#.#.....#.#............... ..............#...#...#...#...#...#...#...#.............. .............#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#............. ............#...............................#............ ...........#.#.............................#.#........... ..........#...#...........................#...#.......... .........#.#.#.#.........................#.#.#.#......... ........#.......#.......................#.......#........ .......#.#.....#.#.....................#.#.....#.#....... ......#...#...#...#...................#...#...#...#...... .....#.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.#..... ....#...............#...............#...............#.... ...#.#.............#.#.............#.#.............#.#... ..#...#...........#...#...........#...#...........#...#.. .#.#.#.#.........#.#.#.#.........#.#.#.#.........#.#.#.#. #.......#.......#.......#.......#.......#.......#.......# ##.....#.#.....#.#.....#.#.....#.#.....#.#.....#.#.....## .##...#...#...#...#...#...#...#...#...#...#...#...#...##. ####.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.####
jq
For simplicity we will use strings of 0s and 1s to represent the automaton, its states, and the rules, except that the "automaton" function will accept decimal rule specifications.
Helper functions
# The ordinal value of the relevant states:
def states:
{"111": 1, "110": 2, "101": 3, "100": 4, "011": 5, "010": 6, "001": 7, "000": 8};
# Compute the next "state"
# input: a state ("111" or "110" ...)
# rule: the rule represented as a string of 0s and 1s
# output: the next state "0" or "1" depending on the rule
def next(rule):
states[.] as $n | rule[($n-1):$n] ;
# The state of cell $n, using 0-based indexing
def triple($n):
if $n == 0 then .[-1:] + .[0:2]
elif $n == (length-1) then .[-2:] + .[0:1]
else .[$n-1:$n+2]
end;
# input: non-negative decimal integer
# output: 0-1 binary string
def binary_digits:
if . == 0 then "0"
else [recurse( if . == 0 then empty else ./2 | floor end ) % 2 | tostring]
| reverse
| .[1:] # remove the leading 0
| join("")
end ;Main function
# "rule" can be given as a decimal or string of 0s and 1s:
def automaton(rule; steps):
# Compute the rule as a string of length 8
def tos:
if type == "number" then "0000000" + binary_digits else . end
| .[-8:];
# input: the current state of the automaton
# output: its next state
def update(rule):
. as $in
| reduce range(0; length) as $n ("";
. + ($in|triple($n)|next(rule)));
(rule | tos) as $rule
| limit(steps; while(true; update($rule) )) ;
# Example
"0000001000000" # initial state
| automaton($rule; $steps) # $rule and $steps are taken from the command line
| gsub("0"; ".") # pretty print
| gsub("1"; "#")
Command-line Invocation
$ jq -r -n -f program.jq --argjson steps 10 --argjson rule 90
- Output:
"......#......" ".....#.#....." "....#...#...." "...#.#.#.#..." "..#.......#.." ".#.#.....#.#." "#...#...#...#" "##.#.#.#.#.##" ".#.........#." "#.#.......#.#"
Julia
struct Automaton
g₀::Vector{Bool}
rule::Function
Automaton(n::Int) = new(
[c == '#' for c ∈ ".........#........."],
i -> isone.(digits(n; base = 2, pad = 8))[i])
end
Base.iterate(a::Automaton, g = a.g₀) =
g, @. a.rule(4*[g[end];g[1:end-1]] + 2*g + [g[2:end];g[1]] + 1)
Base.show(io::IO, a::Automaton) =
for g in Iterators.take(a, 10)
println(io, join(c ? '#' : '.' for c ∈ g))
end
for n ∈ [90, 30, 14]
println("rule $n:")
show(Automaton(n))
println()
end
- Output:
rule 90: .........#......... ........#.#........ .......#...#....... ......#.#.#.#...... .....#.......#..... ....#.#.....#.#.... ...#...#...#...#... ..#.#.#.#.#.#.#.#.. .#...............#. #.#.............#.# rule 30: .........#......... ........###........ .......##..#....... ......##.####...... .....##..#...#..... ....##.####.###.... ...##..#....#..#... ..##.####..######.. .##..#...###.....#. ##.####.##..#...### rule 14: .........#......... ........##......... .......##.......... ......##........... .....##............ ....##............. ...##.............. ..##............... .##................ ##.................
Kotlin
// version 1.1.51
import java.util.BitSet
const val SIZE = 32
const val LINES = SIZE / 2
const val RULE = 90
fun ruleTest(x: Int) = (RULE and (1 shl (7 and x))) != 0
infix fun Boolean.shl(bitCount: Int) = (if (this) 1 else 0) shl bitCount
fun Boolean.toInt() = if (this) 1 else 0
fun evolve(s: BitSet) {
val t = BitSet(SIZE) // all false by default
t[SIZE - 1] = ruleTest((s[0] shl 2) or (s[SIZE - 1] shl 1) or s[SIZE - 2].toInt())
t[0] = ruleTest((s[1] shl 2) or (s[0] shl 1) or s[SIZE - 1].toInt())
for (i in 1 until SIZE - 1) {
t[i] = ruleTest((s[i + 1] shl 2) or (s[i] shl 1) or s[i - 1].toInt())
}
for (i in 0 until SIZE) s[i] = t[i]
}
fun show(s: BitSet) {
for (i in SIZE - 1 downTo 0) print(if (s[i]) "*" else " ")
println()
}
fun main(args: Array<String>) {
var state = BitSet(SIZE)
state.set(LINES)
println("Rule $RULE:")
repeat(LINES) {
show(state)
evolve(state)
}
}
- Output:
Rule 90:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Lua
local CA = {
state = "..............................#..............................",
bstr = { [0]="...", "..#", ".#.", ".##", "#..", "#.#", "##.", "###" },
new = function(self, rule)
local inst = setmetatable({rule=rule}, self)
for b = 0,7 do
inst[inst.bstr[b]] = rule%2==0 and "." or "#"
rule = math.floor(rule/2)
end
return inst
end,
evolve = function(self)
local n, state, newstate = #self.state, self.state, ""
for i = 1,n do
local nbhd = state:sub((i+n-2)%n+1,(i+n-2)%n+1) .. state:sub(i,i) .. state:sub(i%n+1,i%n+1)
newstate = newstate .. self[nbhd]
end
self.state = newstate
end,
}
CA.__index = CA
ca = { CA:new(18), CA:new(30), CA:new(73), CA:new(129) }
for i = 1, 63 do
print(string.format("%-66s%-66s%-66s%-61s", ca[1].state, ca[2].state, ca[3].state, ca[4].state))
for j = 1, 4 do ca[j]:evolve() end
end
- Output:
..............................#.............................. ..............................#.............................. ..............................#.............................. ..............................#.............................. .............................#.#............................. .............................###............................. #############################...############################# #############################...############################# ............................#...#............................ ............................##..#............................ ............................#.#.#............................ ############################..#..############################ ...........................#.#.#.#........................... ...........................##.####........................... ###########################.......########################### ###########################.......########################### ..........................#.......#.......................... ..........................##..#...#.......................... ..........................#.#####.#.......................... ##########################..#####..########################## .........................#.#.....#.#......................... .........................##.####.###......................... #########################...#...#...######################### #########################....###....######################### ........................#...#...#...#........................ ........................##..#....#..#........................ ........................#.#...#...#.#........................ ########################..##..#..##..######################## .......................#.#.#.#.#.#.#.#....................... .......................##.####..######....................... #######################.....#...#.....####################### #######################...............####################### ......................#...............#...................... ......................##..#...###.....#...................... ......................#.###...#...###.#...................... ######################..#############..###################### .....................#.#.............#.#..................... .....................##.####.##..#...###..................... #####################...#.#.#...#.#.#...##################### #####################....###########....##################### ....................#...#...........#...#.................... ....................##..#....#.####.##..#.................... ....................#.#.......#.......#.#.................... ####################..##..#########..##..#################### ...................#.#.#.#.........#.#.#.#................... ...................##.####..##.#....#.####................... ###################.....#####...#####.....################### ###################........#######........################### 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Mathematica /Wolfram Language
Mathematica provides built-in functions for cellular automata. For example visualizing the first 100 rows of rule 30 on an 8-bit grid with a single initial cell:
ArrayPlot[CellularAutomaton[30, {0, 0, 0, 0, 1, 0, 0, 0}, 100]]
MATLAB
function init = cellularAutomaton(rule, init, n)
init(n + 1, :) = 0;
for k = 1 : n
init(k + 1, :) = bitget(rule, 1 + filter2([4 2 1], init(k, :)));
end
- Output:
>> char(cellularAutomaton(90, ~(-15:15), 15) * 10 + 32)
ans =
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
MiniScript
ElementaryCellularAutomaton = {"state": null, "rules": [], "ruleNum": 0}
ElementaryCellularAutomaton.init = function(n, state)
oneD = new ElementaryCellularAutomaton
oneD.state = state.split("")
oneD.ruleNum = n
oneD.rules = oneD.__createRules(n)
return oneD
end function
ElementaryCellularAutomaton.__createRules = function(n)
bits = self.__bitString(n)
rules = []
for i in range(7,0)
if bits[7-i] == "*" then rules.push(self.__bitString(i,3))
end for
return rules
end function
ElementaryCellularAutomaton.__bitString = function(n, width = 8)
s = ""
while s.len < width
s = char(46 - (n % 2) * 4) + s
n = floor(n / 2)
end while
return s
end function
ElementaryCellularAutomaton.evolve = function
length = self.state.len
newState = []
for i in range(0, length - 1)
s = ""
for j in [-1,0,1]
s += self.state[(i + j + length) % length]
end for
if self.rules.indexOf(s) != null then
newState.push "*"
else
newState.push "."
end if
end for
self.state = newState
end function
ElementaryCellularAutomaton.getState = function
output = self.state.join("")
return output
end function
getAllStates = function(cells)
s = ""
for i in range(0, cells.len - 1)
s += " " + cells[i].getState
end for
return s
end function
// Main program
automata = []
startState = "." * 15 + "*" + "." * 15
s = " "
for i in [30,60,90]
s += " " * 13 + "Rule " + i + " " * 12
automata.push(ElementaryCellularAutomaton.init(i, startState))
end for
print s
for i in range(0, 99)
s = "0" * 2 + str(i)
s = s[-3:]
s += getAllStates(automata)
print s
for j in range(0, automata.len - 1)
automata[j].evolve
end for
end for
// display last evolution
s = "100"
s += getAllStates(automata)
print s
- Output:
Rule 30 Rule 60 Rule 90 000 ...............*............... ...............*............... ...............*............... 001 ..............***.............. ...............**.............. ..............*.*.............. 002 .............**..*............. ...............*.*............. .............*...*............. 003 ............**.****............ ...............****............ ............*.*.*.*............ 004 ...........**..*...*........... ...............*...*........... ...........*.......*........... 005 ..........**.****.***.......... ...............**..**.......... ..........*.*.....*.*.......... 006 .........**..*....*..*......... ...............*.*.*.*......... .........*...*...*...*......... 007 ........**.****..******........ ...............********........ ........*.*.*.*.*.*.*.*........ 008 .......**..*...***.....*....... ...............*.......*....... .......*...............*....... 009 ......**.****.**..*...***...... ...............**......**...... ......*.*.............*.*...... 010 .....**..*....*.****.**..*..... ...............*.*.....*.*..... .....*...*...........*...*..... 011 ....**.****..**.*....*.****.... ...............****....****.... ....*.*.*.*.........*.*.*.*.... 012 ...**..*...***..**..**.*...*... ...............*...*...*...*... ...*.......*.......*.......*... 013 ..**.****.**..***.***..**.***.. ...............**..**..**..**.. ..*.*.....*.*.....*.*.....*.*.. 014 .**..*....*.***...*..***..*..*. ...............*.*.*.*.*.*.*.*. .*...*...*...*...*...*...*...*. 015 **.****..**.*..*.*****..******* ...............**************** *.*.*.*.*.*.*.*.*.*.*.*.*.*.*.* 016 ...*...***..****.*....***...... *..............*............... *.............................* 017 ..***.**..***....**..**..*..... **.............**.............. **...........................** 018 .**...*.***..*..**.***.****.... *.*............*.*............. .**.........................**. 019 **.*.**.*..******..*...*...*... ****...........****............ ****.......................**** 020 *..*.*..****.....****.***.***.* *...*..........*...*........... ...**.....................**... 021 .***.****...*...**....*...*...* **..**.........**..**.......... ..****...................****.. 022 .*...*...*.***.**.*..***.***.** *.*.*.*........*.*.*.*......... .**..**.................**..**. 023 .**.***.**.*...*..****...*...*. ********.......********........ ********...............******** 024 **..*...*..**.*****...*.***.*** *.......*......*.......*....... .......**.............**....... 025 ..****.*****..*....*.**.*...*.. **......**.....**......**...... ......****...........****...... 026 .**....*....****..**.*..**.***. *.*.....*.*....*.*.....*.*..... .....**..**.........**..**..... 027 **.*..***..**...***..****..*..* ****....****...****....****.... ....********.......********.... 028 ...****..***.*.**..***...****** *...*...*...*..*...*...*...*... ...**......**.....**......**... 029 *.**...***...*.*.***..*.**..... **..**..**..**.**..**..**..**.. ..****....****...****....****.. 030 *.*.*.**..*.**.*.*..***.*.*...* *.*.*.*.*.*.*.**.*.*.*.*.*.*.*. .**..**..**..**.**..**..**..**. 031 ..*.*.*.***.*..*.****...*.**.** ***************.*************** ***************.*************** 032 ***.*.*.*...****.*...*.**.*..*. ...............**.............. ..............*.*.............. 033 *...*.*.**.**....**.**.*..****. ...............*.*............. .............*...*............. 034 **.**.*.*..*.*..**..*..****.... ...............****............ ............*.*.*.*............ 035 *..*..*.****.****.******...*..* ...............*...*........... ...........*.......*........... 036 .******.*....*....*.....*.***** ...............**..**.......... ..........*.*.....*.*.......... 037 .*......**..***..***...**.*.... ...............*.*.*.*......... .........*...*...*...*......... 038 ***....**.***..***..*.**..**... ...............********........ ........*.*.*.*.*.*.*.*........ 039 *..*..**..*..***..***.*.***.*.* ...............*.......*....... .......*...............*....... 040 .******.******..***...*.*...*.* ...............**......**...... ......*.*.............*.*...... 041 .*......*.....***..*.**.**.**.* ...............*.*.....*.*..... .....*...*...........*...*..... 042 .**....***...**..***.*..*..*..* ...............****....****.... ....*.*.*.*.........*.*.*.*.... 043 .*.*..**..*.**.***...********** ...............*...*...*...*... ...*.......*.......*.......*... 044 .*.****.***.*..*..*.**......... ...............**..**..**..**.. ..*.*.....*.*.....*.*.....*.*.. 045 **.*....*...*******.*.*........ ...............*.*.*.*.*.*.*.*. .*...*...*...*...*...*...*...*. 046 *..**..***.**.......*.**......* ...............**************** *.*.*.*.*.*.*.*.*.*.*.*.*.*.*.* 047 .***.***...*.*.....**.*.*....** *..............*............... *.............................* 048 .*...*..*.**.**...**..*.**..**. **.............**.............. **...........................** 049 ***.*****.*..*.*.**.***.*.***.* *.*............*.*............. .**.........................**. 050 ....*.....****.*.*..*...*.*...* ****...........****............ ****.......................**** 051 *..***...**....*.*****.**.**.** *...*..........*...*........... ...**.....................**... 052 .***..*.**.*..**.*.....*..*..*. **..**.........**..**.......... ..****...................****.. 053 **..***.*..****..**...********* *.*.*.*........*.*.*.*......... .**..**.................**..**. 054 ..***...****...***.*.**........ ********.......********........ ********...............******** 055 .**..*.**...*.**...*.*.*....... *.......*......*.......*....... .......**.............**....... 056 **.***.*.*.**.*.*.**.*.**...... **......**.....**......**...... ......****...........****...... 057 *..*...*.*.*..*.*.*..*.*.*....* *.*.....*.*....*.*.....*.*..... .....**..**.........**..**..... 058 .****.**.*.****.*.****.*.**..** ****....****...****....****.... ....********.......********.... 059 .*....*..*.*....*.*....*.*.***. *...*...*...*..*...*...*...*... ...**......**.....**......**... 060 ***..*****.**..**.**..**.*.*..* **..**..**..**.**..**..**..**.. ..****....****...****....****.. 061 ...***.....*.***..*.***..*.**** *.*.*.*.*.*.*.**.*.*.*.*.*.*.*. .**..**..**..**.**..**..**..**. 062 *.**..*...**.*..***.*..***.*... ***************.*************** ***************.*************** 063 *.*.****.**..****...****...**.* ...............**.............. ..............*.*.............. 064 ..*.*....*.***...*.**...*.**..* ...............*.*............. .............*...*............. 065 ***.**..**.*..*.**.*.*.**.*.*** ...............****............ ............*.*.*.*............ 066 ....*.***..****.*..*.*.*..*.*.. ...............*...*........... ...........*.......*........... 067 ...**.*..***....****.*.****.**. ...............**..**.......... ..........*.*.....*.*.......... 068 ..**..****..*..**....*.*....*.* ...............*.*.*.*......... .........*...*...*...*......... 069 ***.***...******.*..**.**..**.* ...............********........ ........*.*.*.*.*.*.*.*........ 070 ....*..*.**......****..*.***..* ...............*.......*....... .......*...............*....... 071 *..*****.*.*....**...***.*..*** ...............**......**...... ......*.*.............*.*...... 072 .***.....*.**..**.*.**...****.. ...............*.*.....*.*..... .....*...*...........*...*..... 073 **..*...**.*.***..*.*.*.**...*. ...............****....****.... ....*.*.*.*.........*.*.*.*.... 074 *.****.**..*.*..***.*.*.*.*.**. ...............*...*...*...*... ...*.......*.......*.......*... 075 *.*....*.***.****...*.*.*.*.*.. ...............**..**..**..**.. ..*.*.....*.*.....*.*.....*.*.. 076 *.**..**.*...*...*.**.*.*.*.*** ...............*.*.*.*.*.*.*.*. .*...*...*...*...*...*...*...*. 077 ..*.***..**.***.**.*..*.*.*.*.. ...............**************** *.*.*.*.*.*.*.*.*.*.*.*.*.*.*.* 078 .**.*..***..*...*..****.*.*.**. *..............*............... *.............................* 079 **..****..****.*****....*.*.*.* **.............**.............. **...........................** 080 ..***...***....*....*..**.*.*.* *.*............*.*............. .**.........................**. 081 ***..*.**..*..***..*****..*.*.* ****...........****............ ****.......................**** 082 ...***.*.******..***....***.*.* *...*..........*...*........... ...**.....................**... 083 *.**...*.*.....***..*..**...*.* **..**.........**..**.......... ..****...................****.. 084 ..*.*.**.**...**..******.*.**.* *.*.*.*........*.*.*.*......... .**..**.................**..**. 085 ***.*.*..*.*.**.***......*.*..* ********.......********........ ********...............******** 086 ....*.****.*.*..*..*....**.**** *.......*......*.......*....... .......**.............**....... 087 *..**.*....*.********..**..*... **......**.....**......**...... ......****...........****...... 088 ****..**..**.*.......***.****.* *.*.....*.*....*.*.....*.*..... .....**..**.........**..**..... 089 ....***.***..**.....**...*....* ****....****...****....****.... ....********.......********.... 090 *..**...*..***.*...**.*.***..** *...*...*...*..*...*...*...*... ...**......**.....**......**... 091 .***.*.*****...**.**..*.*..***. **..**..**..**.**..**..**..**.. ..****....****...****....****.. 092 **...*.*....*.**..*.***.****..* *.*.*.*.*.*.*.**.*.*.*.*.*.*.*. .**..**..**..**.**..**..**..**. 093 ..*.**.**..**.*.***.*...*...*** ***************.*************** ***************.*************** 094 ***.*..*.***..*.*...**.***.**.. ...............**.............. ..............*.*.............. 095 *...****.*..***.**.**..*...*.** ...............*.*............. .............*...*............. 096 .*.**....****...*..*.****.**.*. ...............****............ ............*.*.*.*............ 097 **.*.*..**...*.*****.*....*..** ...............*...*........... ...........*.......*........... 098 ...*.****.*.**.*.....**..*****. ...............**..**.......... ..........*.*.....*.*.......... 099 ..**.*....*.*..**...**.***....* ...............*.*.*.*......... .........*...*...*...*......... 100 ***..**..**.****.*.**..*..*..** ...............********........ ........*.*.*.*.*.*.*.*........
Nim
import bitops
const
Size = 32
LastBit = Size - 1
Lines = Size div 2
Rule = 90
type State = int # State is represented as an int and will be used as a bit string.
#---------------------------------------------------------------------------------------------------
template bitVal(state: State; n: typed): int =
## Return the value of a bit as an int rather than a bool.
ord(state.testBit(n))
#---------------------------------------------------------------------------------------------------
proc ruleTest(x: int): bool =
## Return true if a bit must be set.
(Rule and 1 shl (7 and x)) != 0
#---------------------------------------------------------------------------------------------------
proc evolve(state: var State) =
## Compute next state.
var newState: State # All bits cleared by default.
if ruleTest(state.bitVal(0) shl 2 or state.bitVal(LastBit) shl 1 or state.bitVal(LastBit-1)):
newState.setBit(LastBit)
if ruleTest(state.bitVal(1) shl 2 or state.bitVal(0) shl 1 or state.bitVal(LastBit)):
newState.setBit(0)
for i in 1..<LastBit:
if ruleTest(state.bitVal(i + 1) shl 2 or state.bitVal(i) shl 1 or state.bitVal(i - 1)):
newState.setBit(i)
state = newState
#---------------------------------------------------------------------------------------------------
proc show(state: State) =
## Show the current state.
for i in countdown(LastBit, 0):
stdout.write if state.testbit(i): '*' else: ' '
echo ""
#———————————————————————————————————————————————————————————————————————————————————————————————————
var state: State
state.setBit(Lines)
echo "Rule ", Rule
for _ in 1..Lines:
show(state)
evolve(state)
- Output:
Rule 90
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Octave
clear all
E=200;
idx=round(E/2);
z(1:1:E^2)=0; % init lattice
z(idx)=1; % seed apex of triangle with a single cell
A=2; % Number of bits-1 rule30 uses 3 so A=2
for n=1:1:E^2/2-E-2; % n=lines
theta=0; % theta
for a=0:1:A;
theta=theta+2^a*z(n+A-a);
endfor
x=(asin(sin (pi/4*(theta-3/4))));
z(n+E+1)=round( (4*x+pi)/(2*pi) );
endfor
imagesc(reshape(z,E,E)'); % Medland map
Perl
use strict;
use warnings;
package Automaton {
sub new {
my $class = shift;
my $rule = [ reverse split //, sprintf "%08b", shift ];
return bless { rule => $rule, cells => [ @_ ] }, $class;
}
sub next {
my $this = shift;
my @previous = @{$this->{cells}};
$this->{cells} = [
@{$this->{rule}}[
map {
4*$previous[($_ - 1) % @previous]
+ 2*$previous[$_]
+ $previous[($_ + 1) % @previous]
} 0 .. @previous - 1
]
];
return $this;
}
use overload
q{""} => sub {
my $this = shift;
join '', map { $_ ? '#' : ' ' } @{$this->{cells}}
};
}
my @a = map 0, 1 .. 91; $a[45] = 1;
my $a = Automaton->new(90, @a);
for (1..40) {
print "|$a|\n"; $a->next;
}
- Output:
| # | | # # | | # # | | # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # # # | | # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # # # | | # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # # # | | # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # # # # # # # # # # # # # # # | | # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # # # | | # # # # # # # # | | # # # # # # # # | | # # # # # # # # # # # # # # # # |
Phix
String-based solution
with javascript_semantics string s = ".........#.........", t = s, r = "........" integer rule = 90, k, l = length(s) for i=1 to 8 do r[i] = iff(mod(rule,2)?'#':'.') rule = floor(rule/2) end for for i=0 to 50 do ?s for j=1 to l do k = (s[iff(j=1?l:j-1)]='#')*4 + (s[ j ]='#')*2 + (s[iff(j=l?1:j+1)]='#')+1 t[j] = r[k] end for s = t end for
Output matches that of D and Python:wrap for rule = 90, 30, 122 (if you edit/run 3 times)
PicoLisp
(de dictionary (N)
(extract
'((A B)
(and
(= "1" B)
(mapcar
'((L) (if (= "1" L) "#" "."))
A ) ) )
(mapcar
'((N) (chop (pad 3 (bin N))))
(range 7 0) )
(chop (pad 8 (bin N))) ) )
(de cellular (Lst N)
(let (Lst (chop Lst) D (dictionary N))
(do 10
(prinl Lst)
(setq Lst
(make
(map
'((L)
(let Y (head 3 L)
(and
(cddr Y)
(link (if (member Y D) "#" ".")) ) ) )
(conc (cons (last Lst)) Lst (cons (car Lst))) ) ) ) ) ) )
(cellular
".........#........."
90 )- Output:
.........#......... ........#.#........ .......#...#....... ......#.#.#.#...... .....#.......#..... ....#.#.....#.#.... ...#...#...#...#... ..#.#.#.#.#.#.#.#.. .#...............#. #.#.............#.#
Prolog
play :- initial(I), do_auto(50, I).
initial([0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]).
do_auto(0, _) :- !.
do_auto(N, I) :-
maplist(writ, I), nl,
apply_rules(I, Next),
succ(N1, N),
do_auto(N1, Next).
r(0,0,0,0).
r(0,0,1,1).
r(0,1,0,0).
r(0,1,1,1).
r(1,0,0,1).
r(1,0,1,0).
r(1,1,0,1).
r(1,1,1,0).
apply_rules(In, Out) :-
apply1st(In, First),
Out = [First|_],
apply(In, First, First, Out).
apply1st([A,B|T], A1) :- last([A,B|T], Last), r(Last,A,B,A1).
apply([A,B], Prev, First, [Prev, This]) :- r(A,B,First,This).
apply([A,B,C|T], Prev, First, [Prev,This|Rest]) :- r(A,B,C,This), apply([B,C|T], This, First, [This|Rest]).
writ(0) :- write('.').
writ(1) :- write(1).
Python
Python: Zero padded
Note: This only fitted the original task description that read:
- You can deal with the limit conditions (what happens on the borders of the space) in any way you please.
def eca(cells, rule):
lencells = len(cells)
c = "0" + cells + "0" # Zero pad the ends
rulebits = '{0:08b}'.format(rule)
neighbours2next = {'{0:03b}'.format(n):rulebits[::-1][n] for n in range(8)}
yield c[1:-1]
while True:
c = ''.join(['0',
''.join(neighbours2next[c[i-1:i+2]]
for i in range(1,lencells+1)),
'0'])
yield c[1:-1]
if __name__ == '__main__':
lines, start, rules = 50, '0000000001000000000', (90, 30, 122)
zipped = [range(lines)] + [eca(start, rule) for rule in rules]
print('\n Rules: %r' % (rules,))
for data in zip(*zipped):
i = data[0]
cells = data[1:]
print('%2i: %s' % (i, ' '.join(cells).replace('0', '.').replace('1', '#')))
- Output:
(Note how Rule 30 does not look random).
Rules: (90, 30, 122) 0: .........#......... .........#......... .........#......... 1: ........#.#........ ........###........ ........#.#........ 2: .......#...#....... .......##..#....... .......#.#.#....... 3: ......#.#.#.#...... ......##.####...... ......#.#.#.#...... 4: .....#.......#..... .....##..#...#..... .....#.#.#.#.#..... 5: ....#.#.....#.#.... ....##.####.###.... ....#.#.#.#.#.#.... 6: ...#...#...#...#... ...##..#....#..#... ...#.#.#.#.#.#.#... 7: ..#.#.#.#.#.#.#.#.. ..##.####..######.. ..#.#.#.#.#.#.#.#.. 8: .#...............#. .##..#...###.....#. .#.#.#.#.#.#.#.#.#. 9: #.#.............#.# ##.####.##..#...### #.#.#.#.#.#.#.#.#.# 10: ...#...........#... #..#....#.####.##.. .#.#.#.#.#.#.#.#.#. 11: ..#.#.........#.#.. #####..##.#....#.#. #.#.#.#.#.#.#.#.#.# 12: .#...#.......#...#. #....###..##..##.## .#.#.#.#.#.#.#.#.#. 13: #.#.#.#.....#.#.#.# ##..##..###.###..#. #.#.#.#.#.#.#.#.#.# 14: .......#...#....... #.###.###...#..#### .#.#.#.#.#.#.#.#.#. 15: ......#.#.#.#...... #.#...#..#.#####... #.#.#.#.#.#.#.#.#.# 16: .....#.......#..... #.##.#####.#....#.. .#.#.#.#.#.#.#.#.#. 17: ....#.#.....#.#.... #.#..#.....##..###. #.#.#.#.#.#.#.#.#.# 18: ...#...#...#...#... #.#####...##.###..# .#.#.#.#.#.#.#.#.#. 19: ..#.#.#.#.#.#.#.#.. #.#....#.##..#..### #.#.#.#.#.#.#.#.#.# 20: .#...............#. #.##..##.#.######.. .#.#.#.#.#.#.#.#.#. 21: #.#.............#.# #.#.###..#.#.....#. #.#.#.#.#.#.#.#.#.# 22: ...#...........#... #.#.#..###.##...### .#.#.#.#.#.#.#.#.#. 23: ..#.#.........#.#.. #.#.####...#.#.##.. #.#.#.#.#.#.#.#.#.# 24: .#...#.......#...#. #.#.#...#.##.#.#.#. .#.#.#.#.#.#.#.#.#. 25: #.#.#.#.....#.#.#.# #.#.##.##.#..#.#.## #.#.#.#.#.#.#.#.#.# 26: .......#...#....... #.#.#..#..####.#.#. .#.#.#.#.#.#.#.#.#. 27: ......#.#.#.#...... #.#.#######....#.## #.#.#.#.#.#.#.#.#.# 28: .....#.......#..... #.#.#......#..##.#. .#.#.#.#.#.#.#.#.#. 29: ....#.#.....#.#.... #.#.##....#####..## #.#.#.#.#.#.#.#.#.# 30: ...#...#...#...#... #.#.#.#..##....###. .#.#.#.#.#.#.#.#.#. 31: ..#.#.#.#.#.#.#.#.. #.#.#.####.#..##..# #.#.#.#.#.#.#.#.#.# 32: .#...............#. #.#.#.#....####.### .#.#.#.#.#.#.#.#.#. 33: #.#.............#.# #.#.#.##..##....#.. #.#.#.#.#.#.#.#.#.# 34: ...#...........#... #.#.#.#.###.#..###. .#.#.#.#.#.#.#.#.#. 35: ..#.#.........#.#.. #.#.#.#.#...####..# #.#.#.#.#.#.#.#.#.# 36: .#...#.......#...#. #.#.#.#.##.##...### .#.#.#.#.#.#.#.#.#. 37: #.#.#.#.....#.#.#.# #.#.#.#.#..#.#.##.. #.#.#.#.#.#.#.#.#.# 38: .......#...#....... #.#.#.#.####.#.#.#. .#.#.#.#.#.#.#.#.#. 39: ......#.#.#.#...... #.#.#.#.#....#.#.## #.#.#.#.#.#.#.#.#.# 40: .....#.......#..... #.#.#.#.##..##.#.#. .#.#.#.#.#.#.#.#.#. 41: ....#.#.....#.#.... #.#.#.#.#.###..#.## #.#.#.#.#.#.#.#.#.# 42: ...#...#...#...#... #.#.#.#.#.#..###.#. .#.#.#.#.#.#.#.#.#. 43: ..#.#.#.#.#.#.#.#.. #.#.#.#.#.####...## #.#.#.#.#.#.#.#.#.# 44: .#...............#. #.#.#.#.#.#...#.##. .#.#.#.#.#.#.#.#.#. 45: #.#.............#.# #.#.#.#.#.##.##.#.# #.#.#.#.#.#.#.#.#.# 46: ...#...........#... #.#.#.#.#.#..#..#.# .#.#.#.#.#.#.#.#.#. 47: ..#.#.........#.#.. #.#.#.#.#.#######.# #.#.#.#.#.#.#.#.#.# 48: .#...#.......#...#. #.#.#.#.#.#.......# .#.#.#.#.#.#.#.#.#. 49: #.#.#.#.....#.#.#.# #.#.#.#.#.##.....## #.#.#.#.#.#.#.#.#.#
Python: wrap
The ends of the cells wrap-around.
def eca_wrap(cells, rule):
lencells = len(cells)
rulebits = '{0:08b}'.format(rule)
neighbours2next = {tuple('{0:03b}'.format(n)):rulebits[::-1][n] for n in range(8)}
c = cells
while True:
yield c
c = ''.join(neighbours2next[(c[i-1], c[i], c[(i+1) % lencells])] for i in range(lencells))
if __name__ == '__main__':
lines, start, rules = 50, '0000000001000000000', (90, 30, 122)
zipped = [range(lines)] + [eca_wrap(start, rule) for rule in rules]
print('\n Rules: %r' % (rules,))
for data in zip(*zipped):
i = data[0]
cells = data[1:]
print('%2i: %s' % (i, ' '.join(cells).replace('0', '.').replace('1', '#')))
- Output:
Rules: (90, 30, 122) 0: .........#......... .........#......... .........#......... 1: ........#.#........ ........###........ ........#.#........ 2: .......#...#....... .......##..#....... .......#.#.#....... 3: ......#.#.#.#...... ......##.####...... ......#.#.#.#...... 4: .....#.......#..... .....##..#...#..... .....#.#.#.#.#..... 5: ....#.#.....#.#.... ....##.####.###.... ....#.#.#.#.#.#.... 6: ...#...#...#...#... ...##..#....#..#... ...#.#.#.#.#.#.#... 7: ..#.#.#.#.#.#.#.#.. ..##.####..######.. ..#.#.#.#.#.#.#.#.. 8: .#...............#. .##..#...###.....#. .#.#.#.#.#.#.#.#.#. 9: #.#.............#.# ##.####.##..#...### #.#.#.#.#.#.#.#.#.# 10: #..#...........#..# ...#....#.####.##.. ##.#.#.#.#.#.#.#.## 11: ###.#.........#.### ..###..##.#....#.#. .##.#.#.#.#.#.#.##. 12: ..#..#.......#..#.. .##..###..##..##.## ####.#.#.#.#.#.#### 13: .#.##.#.....#.##.#. .#.###..###.###..#. ...##.#.#.#.#.##... 14: #..##..#...#..##..# ##.#..###...#..#### ..####.#.#.#.####.. 15: #######.#.#.####### ...####..#.#####... .##..##.#.#.##..##. 16: ......#.....#...... ..##...###.#....#.. ########.#.######## 17: .....#.#...#.#..... .##.#.##...##..###. .......##.##....... 18: ....#...#.#...#.... ##..#.#.#.##.###..# ......#######...... 19: ...#.#.#...#.#.#... ..###.#.#.#..#..### .....##.....##..... 20: ..#.....#.#.....#.. ###...#.#.#######.. ....####...####.... 21: .#.#...#...#...#.#. #..#.##.#.#......## ...##..##.##..##... 22: #...#.#.#.#.#.#...# .###.#..#.##....##. ..###############.. 23: ##.#...........#.## ##...####.#.#..##.# .##.............##. 24: .#..#.........#..#. ..#.##....#.####..# ####...........#### 25: #.##.#.......#.##.# ###.#.#..##.#...### ...##.........##... 26: #.##..#.....#..##.# ....#.####..##.##.. ..####.......####.. 27: #.####.#...#.####.# ...##.#...###..#.#. .##..##.....##..##. 28: #.#..#..#.#..#..#.# ..##..##.##..###.## ########...######## 29: #..##.##...##.##..# ###.###..#.###...#. .......##.##....... 30: #####.###.###.##### #...#..###.#..#.##. ......#######...... 31: ....#.#.#.#.#.#.... ##.#####...####.#.. .....##.....##..... 32: ...#...........#... #..#....#.##....### ....####...####.... 33: ..#.#.........#.#.. .####..##.#.#..##.. ...##..##.##..##... 34: .#...#.......#...#. ##...###..#.####.#. ..###############.. 35: #.#.#.#.....#.#.#.# #.#.##..###.#....#. .##.............##. 36: #......#...#......# #.#.#.###...##..##. ####...........#### 37: ##....#.#.#.#....## #.#.#.#..#.##.###.. ...##.........##... 38: .##..#.......#..##. #.#.#.####.#..#..## ..####.......####.. 39: #####.#.....#.##### ..#.#.#....#######. .##..##.....##..##. 40: ....#..#...#..#.... .##.#.##..##......# ########...######## 41: ...#.##.#.#.##.#... .#..#.#.###.#....## .......##.##....... 42: ..#..##.....##..#.. .####.#.#...##..##. ......#######...... 43: .#.#####...#####.#. ##....#.##.##.###.# .....##.....##..... 44: #..#...##.##...#..# ..#..##.#..#..#...# ....####...####.... 45: ###.#.###.###.#.### ######..########.## ...##..##.##..##... 46: ..#...#.#.#.#...#.. ......###........#. ..###############.. 47: .#.#.#.......#.#.#. .....##..#......### .##.............##. 48: #.....#.....#.....# #...##.####....##.. ####...........#### 49: ##...#.#...#.#...## ##.##..#...#..##.## ...##.........##...
Python: Infinite
Note: This only fitted the original task description that read:
- You can deal with the limit conditions (what happens on the borders of the space) in any way you please.
Pad and extend with inverse of end cells on each iteration.
def _notcell(c):
return '0' if c == '1' else '1'
def eca_infinite(cells, rule):
lencells = len(cells)
rulebits = '{0:08b}'.format(rule)
neighbours2next = {'{0:03b}'.format(n):rulebits[::-1][n] for n in range(8)}
c = cells
while True:
yield c
c = _notcell(c[0])*2 + c + _notcell(c[-1])*2 # Extend and pad the ends
c = ''.join(neighbours2next[c[i-1:i+2]] for i in range(1,len(c) - 1))
#yield c[1:-1]
if __name__ == '__main__':
lines, start, rules = 20, '1', (90, 30, 122)
zipped = [range(lines)] + [eca_infinite(start, rule) for rule in rules]
print('\n Rules: %r' % (rules,))
for data in zip(*zipped):
i = data[0]
cells = ['%s%s%s' % (' '*(lines - i), c, ' '*(lines - i)) for c in data[1:]]
print('%2i: %s' % (i, ' '.join(cells).replace('0', '.').replace('1', '#')))
- Output:
Rules: (90, 30, 122) 0: # # # 1: #.# ### #.# 2: #...# ##..# #.#.# 3: #.#.#.# ##.#### #.#.#.# 4: #.......# ##..#...# #.#.#.#.# 5: #.#.....#.# ##.####.### #.#.#.#.#.# 6: #...#...#...# ##..#....#..# #.#.#.#.#.#.# 7: #.#.#.#.#.#.#.# ##.####..###### #.#.#.#.#.#.#.# 8: #...............# ##..#...###.....# #.#.#.#.#.#.#.#.# 9: #.#.............#.# ##.####.##..#...### #.#.#.#.#.#.#.#.#.# 10: #...#...........#...# ##..#....#.####.##..# #.#.#.#.#.#.#.#.#.#.# 11: #.#.#.#.........#.#.#.# ##.####..##.#....#.#### #.#.#.#.#.#.#.#.#.#.#.# 12: #.......#.......#.......# ##..#...###..##..##.#...# #.#.#.#.#.#.#.#.#.#.#.#.# 13: #.#.....#.#.....#.#.....#.# ##.####.##..###.###..##.### #.#.#.#.#.#.#.#.#.#.#.#.#.# 14: #...#...#...#...#...#...#...# ##..#....#.###...#..###..#..# #.#.#.#.#.#.#.#.#.#.#.#.#.#.# 15: #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# ##.####..##.#..#.#####..####### #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 16: #...............................# ##..#...###..####.#....###......# #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 17: #.#.............................#.# ##.####.##..###....##..##..#....### #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 18: #...#...........................#...# ##..#....#.###..#..##.###.####..##..# #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 19: #.#.#.#.........................#.#.#.# ##.####..##.#..######..#...#...###.#### #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 20: #.......#.......................#.......# ##..#...###..####.....####.###.##...#...# #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 21: #.#.....#.#.....................#.#.....#.# ##.####.##..###...#...##....#...#.#.###.### #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 22: #...#...#...#...................#...#...#...# ##..#....#.###..#.###.##.#..###.##.#.#...#..# #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 23: #.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.# ##.####..##.#..###.#...#..####...#..#.##.###### #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 24: #...............#...............#...............# ##..#...###..####...##.#####...#.#####.#..#.....# #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
Quackery
( the Cellular Automaton is on the stack as 3 items, the )
( Rule (R), the Size of the space (S) and the Current )
( state (C). make-ca sets this up from a string indicating )
( the size and starting state, and a rule number. )
[ [] swap
8 times
[ dup 1 &
rot swap join
swap 1 >> ]
drop swap
dup size swap
0 swap reverse
witheach
[ char # =
dip [ 1 << ]
+ ] ] is make-ca ( $ n --> R S C )
[ $ "" unrot
swap times
[ dup 1 & iff
[ char # ]
else
[ char . ]
rot join swap
1 >> ]
drop echo$ cr ] is echo-ca ( S C --> )
[ dip bit
2dup 1 & iff
| else drop
1 << swap
over & 0 != | ] is wrap ( S C --> C )
[ rot temp put
dip dup 0 unrot wrap
rot times
[ dup 7 &
temp share swap peek if
[ i^ bit rot | swap ]
1 >> ]
drop temp release ] is next-ca ( R S C --> C )
[ dip
[ over echo$ cr
make-ca ]
1 - times
[ dip 2dup next-ca
2dup echo-ca ]
2drop drop ] is generations ( $ n n --> )
say "Rule 30, 50 generations:" cr cr
$ ".........#........." 30 50 generations- Output:
Rule 30, 50 generations: .........#......... ........###........ .......##..#....... ......##.####...... .....##..#...#..... ....##.####.###.... ...##..#....#..#... ..##.####..######.. .##..#...###.....#. ##.####.##..#...### ...#....#.####.##.. ..###..##.#....#.#. .##..###..##..##.## .#.###..###.###..#. ##.#..###...#..#### ...####..#.#####... ..##...###.#....#.. .##.#.##...##..###. ##..#.#.#.##.###..# ..###.#.#.#..#..### ###...#.#.#######.. #..#.##.#.#......## .###.#..#.##....##. ##...####.#.#..##.# ..#.##....#.####..# ###.#.#..##.#...### ....#.####..##.##.. ...##.#...###..#.#. ..##..##.##..###.## ###.###..#.###...#. #...#..###.#..#.##. ##.#####...####.#.. #..#....#.##....### .####..##.#.#..##.. ##...###..#.####.#. #.#.##..###.#....#. #.#.#.###...##..##. #.#.#.#..#.##.###.. #.#.#.####.#..#..## ..#.#.#....#######. .##.#.##..##......# .#..#.#.###.#....## .####.#.#...##..##. ##....#.##.##.###.# ..#..##.#..#..#...# ######..########.## ......###........#. .....##..#......### #...##.####....##.. ##.##..#...#..##.##
Racket
This is the base code for the three elementary CA tasks. The "wrap" code is a little over-complicated for the simple cases of wrapping on word boundaries and for CA's with a narrower word. However, it will be used unmodified for Elementary cellular automaton/Infinite length.
#lang racket
(require racket/fixnum)
(provide usable-bits/fixnum usable-bits/fixnum-1 CA-next-generation
wrap-rule-truncate-left-word show-automaton)
(define usable-bits/fixnum 30)
(define usable-bits/fixnum-1 (sub1 usable-bits/fixnum))
(define usable-bits/mask (fx- (fxlshift 1 usable-bits/fixnum) 1))
(define 2^u-b-1 (fxlshift 1 usable-bits/fixnum-1))
(define (fxior3 a b c) (fxior (fxior a b) c))
(define (if-bit-set n i [result 1]) (if (bitwise-bit-set? n i) result 0))
(define (shift-right-1-bit-with-lsb-L L n)
(fxior (if-bit-set L 0 2^u-b-1) (fxrshift n 1)))
(define (shift-left-1-bit-with-msb-R n R)
(fxior (fxand usable-bits/mask (fxlshift n 1))
(if-bit-set R usable-bits/fixnum-1)))
(define ((CA-next-bit-state rule) L n R)
(for/fold ([n+ 0])
([b (in-range usable-bits/fixnum-1 -1 -1)])
(define rule-bit (fxior3 (if-bit-set (shift-right-1-bit-with-lsb-L L n) b 4)
(if-bit-set n b 2)
(if-bit-set (shift-left-1-bit-with-msb-R n R) b)))
(fxior (fxlshift n+ 1) (if-bit-set rule rule-bit))))
;; CA-next-generation generates a function which takes:
;; v-in : an fxvector representing the CA's current state as a bit field. This may be mutated
;; offset : the offset of the leftmost element of v-in; this is used in infinite CA to allow the CA
;; to occupy negative indices
;; wrap-rule : provided for automata that are not an integer number of usable-bits/fixnum bits wide
;; wrap-rule = #f - v-in and offset are unchanged
;; wrap-rule : (v-in vl-1 offset) -> (values v-out vl-1+ offset-)
;; v-in as passed into CA-next-generation
;; vl-1=(sub1 (length v-in)), since its precomputed vaule is needed
;; offset as passed into CA-next-generation
;; v-out: either a new copy of v-in, or v-in itself (which might be mutated)
;; vl-1+: (sub1 (length v-out))
;; offset- : a new value for offset (it will have decreased since the CA grows to the left
;; with offset, and to the right with (length v-out)
(define (CA-next-generation rule #:wrap-rule (wrap-rule values))
(define next-state (CA-next-bit-state rule))
(lambda (v-in offset)
(define vl-1 (fx- (fxvector-length v-in) 1))
(define-values [v+ v+l-1 offset-] (wrap-rule v-in vl-1 offset))
(define rv
(for/fxvector ([l (in-sequences (in-value (fxvector-ref v+ v+l-1)) (in-fxvector v+))]
[n (in-fxvector v+)]
[r (in-sequences (in-fxvector v+ 1) (in-value (fxvector-ref v+ 0)))])
(next-state l n r)))
(values rv offset-)))
;; CA-next-generation with the default (non) wrap rule wraps the MSB of the left-hand word (L) and the
;; LSB of the right-hand word (R) in the CA. If the CA is not a multiple of usable-bits/fixnum wide,
;; then we use this function to put these bits where they can be used... i.e. the actual MSB is copied
;; to the word's MSB and the LSB is copied to the bit that is to the left of the actual MSB.
(define (wrap-rule-truncate-left-word sig-bits)
(define wlb-mask (fx- (fxlshift 1 sig-bits) 1))
(unless (fx< sig-bits (fx- usable-bits/fixnum 1))
(error "we need at least 2 bits in the top of the word to do this safely"))
(lambda (v-in vl-1 offset)
(define v0 (fxvector-ref v-in 0))
;; this must wrap to wlb of the first word
(define last-bit (fxlshift (fxand 1 (fxvector-ref v-in vl-1)) sig-bits))
;; this must wrap to the extreme left of the first word
(define first-bit (if-bit-set v0 (fx- sig-bits 1) 2^u-b-1))
(fxvector-set! v-in 0 (fxior3 last-bit first-bit (fxand v0 wlb-mask)))
(values v-in vl-1 offset)))
;; This displays a state of the CA
(define (show-automaton v #:step (step #f) #:sig-bits (sig-bits #f) #:push-right (push-right #f))
(when step (printf "[~a] " (~a #:align 'right #:width 10 step)))
(when push-right (display (make-string (* usable-bits/fixnum push-right) #\.)))
(when (number? sig-bits)
(display (~a #:width sig-bits #:align 'right #:pad-string "0"
(number->string (fxvector-ref v 0) 2))))
(for ([n (in-fxvector v (if sig-bits 1 0))])
(display (~a #:width usable-bits/fixnum #:align 'right #:pad-string "0" (number->string n 2)))))
(module+ main
(define ng/122/19-bits (CA-next-generation 122 #:wrap-rule (wrap-rule-truncate-left-word 19)))
(for/fold ([v (fxvector #b1000000000)] [o 0]) ([step (in-range 40)])
(show-automaton v #:step step #:sig-bits 19)
(newline)
(ng/122/19-bits v o)))
- Output:
[ 0] 0000000001000000000 [ 1] 0000000010100000000 [ 2] 0000000101010000000 [ 3] 0000001010101000000 [ 4] 0000010101010100000 [ 5] 0000101010101010000 [ 6] 0001010101010101000 [ 7] 0010101010101010100 [ 8] 0101010101010101010 [ 9] 1010101010101010101 [ 10] 1100000001111010101 [ 11] 1100000001101101010 [ 12] 1111010101010101111 [ 13] 1100000001100011010 [ 14] 0011110101010111100 [ 15] 0110011010101100110 [ 16] 1111111101011111111 [ 17] 1100000001100000001 [ 18] 0000001111111000000 [ 19] 0000011000001100000 [ 20] 0000111100011110000 [ 21] 0001100110110011000 [ 22] 0011111111111111100 [ 23] 0110000000000000110 [ 24] 1111000000000001111 [ 25] 1100000001100011000 [ 26] 0011110000000111100 [ 27] 0110011000001100110 [ 28] 1111111100011111111 [ 29] 1100000001100000001 [ 30] 0000001111111000000 [ 31] 0000011000001100000 [ 32] 0000111100011110000 [ 33] 0001100110110011000 [ 34] 0011111111111111100 [ 35] 0110000000000000110 [ 36] 1111000000000001111 [ 37] 1100000001100011000 [ 38] 0011110000000111100 [ 39] 0110011000001100110 #fx(522495) 0
Raku
(formerly Perl 6)
Using the Automaton class defined at One-dimensional_cellular_automata#Raku:
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)
]
)
}
}
my @padding = 0 xx 10;
my Automaton $a .= new:
:rule(30),
:cells(flat @padding, 1, @padding);
say $a++ for ^10;
- Output:
| # | | ### | | ## # | | ## #### | | ## # # | | ## #### ### | | ## # # # | | ## #### ###### | | ## # ### # | | ## #### ## # ### |
Ruby
class ElemCellAutomat
include Enumerable
def initialize (start_str, rule, disp=false)
@cur = start_str
@patterns = Hash[8.times.map{|i|["%03b"%i, "01"[rule[i]]]}]
puts "Rule (#{rule}) : #@patterns" if disp
end
def each
return to_enum unless block_given?
loop do
yield @cur
str = @cur[-1] + @cur + @cur[0]
@cur = @cur.size.times.map {|i| @patterns[str[i,3]]}.join
end
end
end
eca = ElemCellAutomat.new('1'.center(39, "0"), 18, true)
eca.take(30).each{|line| puts line.tr("01", ".#")}
- Output:
Rule (18) : {"000"=>"0", "001"=>"1", "010"=>"0", "011"=>"0", "100"=>"1", "101"=>"0", "110"=>"0", "111"=>"0"}
...................#...................
..................#.#..................
.................#...#.................
................#.#.#.#................
...............#.......#...............
..............#.#.....#.#..............
.............#...#...#...#.............
............#.#.#.#.#.#.#.#............
...........#...............#...........
..........#.#.............#.#..........
.........#...#...........#...#.........
........#.#.#.#.........#.#.#.#........
.......#.......#.......#.......#.......
......#.#.....#.#.....#.#.....#.#......
.....#...#...#...#...#...#...#...#.....
....#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#....
...#...............................#...
..#.#.............................#.#..
.#...#...........................#...#.
#.#.#.#.........................#.#.#.#
.......#.......................#.......
......#.#.....................#.#......
.....#...#...................#...#.....
....#.#.#.#.................#.#.#.#....
...#.......#...............#.......#...
..#.#.....#.#.............#.#.....#.#..
.#...#...#...#...........#...#...#...#.
#.#.#.#.#.#.#.#.........#.#.#.#.#.#.#.#
...............#.......#...............
..............#.#.....#.#..............
Rust
fn main() {
struct ElementaryCA {
rule: u8,
state: u64,
}
impl ElementaryCA {
fn new(rule: u8) -> (u64, ElementaryCA) {
let out = ElementaryCA {
rule,
state: 1,
};
(out.state, out)
}
fn next(&mut self) -> u64 {
let mut next_state = 0u64;
let state = self.state;
for i in 0..64 {
next_state |= (((self.rule as u64)>>(7 & (state.rotate_left(1).rotate_right(i as u32)))) & 1)<<i;
}
self.state = next_state;
self.state
}
}
fn rep_u64(val: u64) -> String {
let mut out = String::new();
for i in (0..64).rev() {
if 1<<i & val != 0 {
out = out + "\u{2588}";
} else {
out = out + "-";
}
}
out
}
let (i, mut thirty) = ElementaryCA::new(154);
println!("{}",rep_u64(i));
for _ in 0..32 {
let s = thirty.next();
println!("{}", rep_u64(s));
}
}
- Output:
---------------------------------------------------------------█ █-------------------------------------------------------------█- -█-----------------------------------------------------------█-- █-█---------------------------------------------------------█-█- ---█-------------------------------------------------------█---- --█-█-----------------------------------------------------█-█--- -█---█---------------------------------------------------█---█-- █-█-█-█-------------------------------------------------█-█-█-█- -------█-----------------------------------------------█-------- ------█-█---------------------------------------------█-█------- -----█---█-------------------------------------------█---█------ ----█-█-█-█-----------------------------------------█-█-█-█----- ---█-------█---------------------------------------█-------█---- --█-█-----█-█-------------------------------------█-█-----█-█--- -█---█---█---█-----------------------------------█---█---█---█-- █-█-█-█-█-█-█-█---------------------------------█-█-█-█-█-█-█-█- ---------------█-------------------------------█---------------- --------------█-█-----------------------------█-█--------------- -------------█---█---------------------------█---█-------------- ------------█-█-█-█-------------------------█-█-█-█------------- -----------█-------█-----------------------█-------█------------ ----------█-█-----█-█---------------------█-█-----█-█----------- ---------█---█---█---█-------------------█---█---█---█---------- --------█-█-█-█-█-█-█-█-----------------█-█-█-█-█-█-█-█--------- -------█---------------█---------------█---------------█-------- ------█-█-------------█-█-------------█-█-------------█-█------- -----█---█-----------█---█-----------█---█-----------█---█------ ----█-█-█-█---------█-█-█-█---------█-█-█-█---------█-█-█-█----- ---█-------█-------█-------█-------█-------█-------█-------█---- --█-█-----█-█-----█-█-----█-█-----█-█-----█-█-----█-█-----█-█--- -█---█---█---█---█---█---█---█---█---█---█---█---█---█---█---█-- █-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█-█- ----------------------------------------------------------------
Scala
Java Swing Interoperability
import java.awt._
import java.awt.event.ActionEvent
import javax.swing._
object ElementaryCellularAutomaton extends App {
SwingUtilities.invokeLater(() =>
new JFrame("Elementary Cellular Automaton") {
class ElementaryCellularAutomaton extends JPanel {
private val dim = new Dimension(900, 450)
private val cells = Array.ofDim[Byte](dim.height, dim.width)
private var rule = 0
private def ruleSet =
Seq(30, 45, 50, 57, 62, 70, 73, 75, 86, 89, 90, 99, 101, 105, 109, 110, 124, 129, 133, 135, 137, 139, 141, 164, 170, 232)
override def paintComponent(gg: Graphics): Unit = {
def drawCa(g: Graphics2D): Unit = {
def rules(lhs: Int, mid: Int, rhs: Int) = {
val idx = lhs << 2 | mid << 1 | rhs
(ruleSet(rule) >> idx & 1).toByte
}
g.setColor(Color.black)
for (r <- 0 until cells.length - 1;
c <- 1 until cells(r).length - 1;
lhs = cells(r)(c - 1);
mid = cells(r)(c);
rhs = cells(r)(c + 1)) {
cells(r + 1)(c) = rules(lhs, mid, rhs) // next generation
if (cells(r)(c) == 1) g.fillRect(c, r, 1, 1)
}
}
def drawLegend(g: Graphics2D): Unit = {
val s = ruleSet(rule).toString
val sw = g.getFontMetrics.stringWidth(ruleSet(rule).toString)
g.setColor(Color.white)
g.fillRect(16, 5, 55, 30)
g.setColor(Color.darkGray)
g.drawString(s, 16 + (55 - sw) / 2, 30)
}
super.paintComponent(gg)
val g = gg.asInstanceOf[Graphics2D]
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawCa(g)
drawLegend(g)
}
new Timer(5000, (_: ActionEvent) => {
rule += 1
if (rule == ruleSet.length) rule = 0
repaint()
}).start()
cells(0)(dim.width / 2) = 1
setBackground(Color.white)
setFont(new Font("SansSerif", Font.BOLD, 28))
setPreferredSize(dim)
}
add(new ElementaryCellularAutomaton, BorderLayout.CENTER)
pack()
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
})
}
Scheme
; uses SRFI-1 library http://srfi.schemers.org/srfi-1/srfi-1.html
(define (evolve ls r)
(unfold
(lambda (x) (null? (cddr x)))
(lambda (x)
(vector-ref r (+ (* 4 (first x)) (* 2 (second x)) (third x))))
cdr
(cons (last ls) (append ls (list (car ls))))))
(define (automaton s r n)
(define (*automaton s0 rv n)
(for-each (lambda (x) (display (if (zero? x) #\. #\#))) s0)
(newline)
(if (not (zero? n))
(let ((s1 (evolve s0 rv)))
(*automaton s1 rv (- n 1)))))
(display "Rule ")
(display r)
(newline)
(*automaton
s
(list->vector
(append
(int->bin r)
(make-list (- 7 (floor (/ (log r) (log 2)))) 0)))
n))
(automaton '(0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1) 30 20)
- Output:
Rule 30 .#...#.#..####.....# .##.##.####...#...## .#..#..#...#.###.##. #########.##.#...#.# ..........#..##.##.# #........#####..#..# .#......##....###### .##....##.#..##..... ##.#..##..####.#.... #..####.###....##..# .###....#..#..##.### .#..#..########..#.. ########.......####. #.......#.....##.... ##.....###...##.#..# ..#...##..#.##..#### ####.##.###.#.###... #....#..#...#.#..#.# .#..######.##.####.# .####......#..#....# .#...#....######..##
Sidef
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 = 20
var arr = size.of(0)
arr[size/2] = 1
var auto = Automaton(90, arr)
(size/2).times {
print "|#{auto}|\n"
auto.next
}
- Output:
| # | | # # | | # # | | # # # # | | # # | | # # # # | | # # # # | | # # # # # # # # | | # # | | # # # #|
Tcl
package require Tcl 8.6
oo::class create ElementaryAutomaton {
variable rules
# Decode the rule number to get a collection of state mapping rules.
# In effect, "compiles" the rule number
constructor {ruleNumber} {
set ins {111 110 101 100 011 010 001 000}
set bits [split [string range [format %08b $ruleNumber] end-7 end] ""]
foreach input {111 110 101 100 011 010 001 000} state $bits {
dict set rules $input $state
}
}
# Apply the rule to an automaton state to get a new automaton state.
# We wrap the edges; the state space is circular.
method evolve {state} {
set len [llength $state]
for {set i 0} {$i < $len} {incr i} {
lappend result [dict get $rules [
lindex $state [expr {($i-1)%$len}]][
lindex $state $i][
lindex $state [expr {($i+1)%$len}]]]
}
return $result
}
# Simple driver method; omit the initial state to get a centred dot
method run {steps {initialState ""}} {
if {[llength [info level 0]] < 4} {
set initialState "[string repeat . $steps]1[string repeat . $steps]"
}
set s [split [string map ". 0 # 1" $initialState] ""]
for {set i 0} {$i < $steps} {incr i} {
puts [string map "0 . 1 #" [join $s ""]]
set s [my evolve $s]
}
puts [string map "0 . 1 #" [join $s ""]]
}
}
Demonstrating:
puts "Rule 90 (with default state):"
ElementaryAutomaton create rule90 90
rule90 run 20
puts "\nRule 122:"
[ElementaryAutomaton new 122] run 25 "..........#......…."
- Output:
Rule 90 (with default state): ....................#.................... ...................#.#................... ..................#...#.................. .................#.#.#.#................. ................#.......#................ ...............#.#.....#.#............... ..............#...#...#...#.............. .............#.#.#.#.#.#.#.#............. ............#...............#............ ...........#.#.............#.#........... ..........#...#...........#...#.......... .........#.#.#.#.........#.#.#.#......... ........#.......#.......#.......#........ .......#.#.....#.#.....#.#.....#.#....... ......#...#...#...#...#...#...#...#...... .....#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..... ....#...............................#.... ...#.#.............................#.#... ..#...#...........................#...#.. .#.#.#.#.........................#.#.#.#. #.......#.......................#.......# Rule 122: ..........#.......... .........#.#......... ........#.#.#........ .......#.#.#.#....... ......#.#.#.#.#...... .....#.#.#.#.#.#..... ....#.#.#.#.#.#.#.... ...#.#.#.#.#.#.#.#... ..#.#.#.#.#.#.#.#.#.. .#.#.#.#.#.#.#.#.#.#. #.#.#.#.#.#.#.#.#.#.# ##.#.#.#.#.#.#.#.#.## .##.#.#.#.#.#.#.#.##. ####.#.#.#.#.#.#.#### ...##.#.#.#.#.#.##... ..####.#.#.#.#.####.. .##..##.#.#.#.##..##. ########.#.#.######## .......##.#.##....... ......####.####...... .....##..###..##..... ....######.######.... ...##....###....##... ..####..##.##..####.. .##..###########..##. ######.........######
UNIX Shell
function print_cells {
local chars=(. '#') cell
for cell; do
printf '%s' "${chars[$cell]}"
done
printf '\n'
}
function next_gen {
local rule=$1
shift
cells=("$@")
local -i l c r bit
for (( l=$#-1, c=0, r=1; c < $#;
l=(l+1)%$#, c+=1, r=(r+1)%$# )); do
local left=${cells[l]} current=${cells[c]} right=${cells[r]}
(( bit = 1<<(left<<2 | current<<1 | right) ))
printf '%d\n' $(( rule & bit ? 1 : 0 ))
done
}
function automaton {
local size=${1:-32} rule=${2:-90}
local stop=${3:-$(( size/2 ))}
local i gen cells=()
for (( i=0; i<size; ++i )); do
cells+=( $(( i == size/2 )) )
done
for (( gen=0; gen<stop; ++gen )); do
printf "%${#stop}d: " "$gen"
print_cells "${cells[@]}"
cells=($(next_gen "$rule" "${cells[@]}"))
done
}
automaton "$@"
- Output:
0: ................#............... 1: ...............#.#.............. 2: ..............#...#............. 3: .............#.#.#.#............ 4: ............#.......#........... 5: ...........#.#.....#.#.......... 6: ..........#...#...#...#......... 7: .........#.#.#.#.#.#.#.#........ 8: ........#...............#....... 9: .......#.#.............#.#...... 10: ......#...#...........#...#..... 11: .....#.#.#.#.........#.#.#.#.... 12: ....#.......#.......#.......#... 13: ...#.#.....#.#.....#.#.....#.#.. 14: ..#...#...#...#...#...#...#...#. 15: .#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
Wren
import "./fmt" for Conv
var SIZE = 32
var LINES = SIZE / 2
var RULE = 90
var ruleTest = Fn.new { |x| (RULE & (1 << (7 & x))) != 0 }
var bshl = Fn.new { |b, bitCount| Conv.btoi(b) << bitCount }
var evolve = Fn.new { |s|
var t = List.filled(SIZE, false)
t[SIZE-1] = ruleTest.call(bshl.call(s[0], 2) | bshl.call(s[SIZE-1], 1) | Conv.btoi(s[SIZE-2]))
t[0] = ruleTest.call(bshl.call(s[1], 2) | bshl.call(s[0], 1) | Conv.btoi(s[SIZE-1]))
for (i in 1...SIZE - 1) {
t[i] = ruleTest.call(bshl.call(s[i+1], 2) | bshl.call(s[i], 1) | Conv.btoi(s[i-1]))
}
for (i in 0...SIZE) s[i] = t[i]
}
var show = Fn.new { |s|
for (i in SIZE - 1..0) System.write(s[i] ? "*" : " ")
System.print()
}
var state = List.filled(SIZE, false)
state[LINES] = true
System.print("Rule %(RULE):")
for (i in 0...LINES) {
show.call(state)
evolve.call(state)
}
- Output:
Rule 90:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
XPL0
def Width = 32, Rule = 90; \ = %0101_1010
int Gen, Old, New, Shift, Triad;
[New:= 1<<(Width/2);
for Gen:= 0 to 15 do
[Old:= New;
repeat ChOut(0, if New&1 then ^* else ^ );
New:= New>>1;
until New = 0;
CrLf(0);
New:= 0; Shift:= 1;
repeat Triad:= Old & %111;
if Rule & 1<<Triad then
New:= New + 1<<Shift;
Old:= Old>>1;
Shift:= Shift+1;
until Shift >= Width;
];
]- Output:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
zkl
fcn rule(n){ n=n.toString(2); "00000000"[n.len() - 8,*] + n }
fcn applyRule(rule,cells){
cells=String(cells[-1],cells,cells[0]); // wrap cell ends
(cells.len() - 2).pump(String,'wrap(n){ rule[7 - cells[n,3].toInt(2)] })
}cells:="0000000000000001000000000000000"; r90:=rule(90); map:=" *";
r90.println(" rule 90");
do(20){ cells.apply(map.get).println(); cells=applyRule(r90,cells); }- Output:
01011010 rule 90
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* *
** **
** **
**** ****
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