# Elementary cellular automaton/Infinite length

Elementary cellular automaton/Infinite length is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The purpose of this task is to create a version of an Elementary cellular automaton whose number of cells is only limited by the memory size of the computer.

To be precise, consider the state of the automaton to be made of an infinite number of cells, but with a bounded support. In other words, to describe the state of the automaton, you need a finite number of adjacent cells, along with their individual state, and you then consider that the individual state of each of all other cells is the negation of the closest individual cell among the previously defined finite number of cells.

Examples:

```1        ->   ..., 0, 0,      1,      0, 0, ...
0, 1     ->   ..., 1, 1,   0, 1,      0, 0, ...
1, 0, 1  ->   ..., 0, 0,   1, 0, 1,   0, 0, ...
```

More complex methods can be imagined, provided it is possible to somehow encode the infinite sections. But for this task we will stick to this simple version.

## C++

` #include <iostream>#include <iomanip>#include <string> class oo {public:    void evolve( int l, int rule ) {        std::string    cells = "O";        std::cout << " Rule #" << rule << ":\n";        for( int x = 0; x < l; x++ ) {            addNoCells( cells );            std::cout << std::setw( 40 + ( static_cast<int>( cells.length() ) >> 1 ) ) << cells << "\n";            step( cells, rule );        }    }private:    void step( std::string& cells, int rule ) {        int bin;        std::string newCells;        for( size_t i = 0; i < cells.length() - 2; i++ ) {            bin = 0;            for( size_t n = i, b = 2; n < i + 3; n++, b >>= 1 ) {                bin += ( ( cells[n] == 'O' ? 1 : 0 ) << b );            }            newCells.append( 1, rule & ( 1 << bin ) ? 'O' : '.' );        }        cells = newCells;    }    void addNoCells( std::string& s ) {        char l = s.at( 0 ) == 'O' ? '.' : 'O',             r = s.at( s.length() - 1 ) == 'O' ? '.' : 'O';        s = l + s + r;        s = l + s + r;    }};int main( int argc, char* argv[] ) {    oo o;    o.evolve( 35, 90 );    std::cout << "\n";    return 0;} `
Output:
```Rule #90:                                                    Rule #30:
..O..                                                        ..O..
..O.O..                                                      ..OOO..
..O...O..                                                    ..OO..O..
..O.O.O.O..                                                  ..OO.OOOO..
..O.......O..                                                ..OO..O...O..
..O.O.....O.O..                                              ..OO.OOOO.OOO..
..O...O...O...O..                                            ..OO..O....O..O..
..O.O.O.O.O.O.O.O..                                          ..OO.OOOO..OOOOOO..
..O...............O..                                        ..OO..O...OOO.....O..
..O.O.............O.O..                                      ..OO.OOOO.OO..O...OOO..
..O...O...........O...O..                                    ..OO..O....O.OOOO.OO..O..
..O.O.O.O.........O.O.O.O..                                  ..OO.OOOO..OO.O....O.OOOO..
..O.......O.......O.......O..                                ..OO..O...OOO..OO..OO.O...O..
..O.O.....O.O.....O.O.....O.O..                              ..OO.OOOO.OO..OOO.OOO..OO.OOO..
..O...O...O...O...O...O...O...O..                            ..OO..O....O.OOO...O..OOO..O..O..
..O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O..                          ..OO.OOOO..OO.O..O.OOOOO..OOOOOOO..
..O...............................O..                        ..OO..O...OOO..OOOO.O....OOO......O..
..O.O.............................O.O..                      ..OO.OOOO.OO..OOO....OO..OO..O....OOO..
..O...O...........................O...O..                    ..OO..O....O.OOO..O..OO.OOO.OOOO..OO..O..
..O.O.O.O.........................O.O.O.O..                  ..OO.OOOO..OO.O..OOOOOO..O...O...OOO.OOOO..
..O.......O.......................O.......O..                ..OO..O...OOO..OOOO.....OOOO.OOO.OO...O...O..
..O.O.....O.O.....................O.O.....O.O..              ..OO.OOOO.OO..OOO...O...OO....O...O.O.OOO.OOO..
..O...O...O...O...................O...O...O...O..            ..OO..O....O.OOO..O.OOO.OO.O..OOO.OO.O.O...O..O..
..O.O.O.O.O.O.O.O.................O.O.O.O.O.O.O.O..          ..OO.OOOO..OO.O..OOO.O...O..OOOO...O..O.OO.OOOOOO..
..O...............O...............O...............O..        ..OO..O...OOO..OOOO...OO.OOOOO...O.OOOOO.O..O.....O..
```

## D

Translation of: Python
`import std.stdio, std.array, std.range, std.typecons, std.string, std.conv,       std.algorithm;alias R = replicate; void main() {    enum nLines = 25;    enum notCell = (in char c) pure => (c == '1') ? "0" : "1";     foreach (immutable rule; [90, 30]) {        writeln("\nRule: ", rule);        immutable ruleBits = "%08b".format(rule).retro.text;        const neighs2next = 8.iota                            .map!(n => tuple("%03b".format(n), [ruleBits[n]]))                            .assocArray;         string C = "1";        foreach (immutable i; 0 .. nLines) {            writefln("%2d: %s%s", i, " ".R(nLines - i), C.tr("01", ".#"));            C = notCell(C[0]).R(2) ~ C ~ notCell(C[\$ - 1]).R(2);            C = iota(1, C.length - 1)                .map!(i => neighs2next[C[i - 1 .. i + 2]])                .join;        }    }}`

The output is the same as the Python entry.

## Elixir

Works with: Elixir version 1.3
Translation of: Ruby
` defmodule Elementary_cellular_automaton do  def infinite(cell, rule, times) do    each(cell, rule_pattern(rule), times)  end   defp each(_, _, 0), do: :ok  defp each(cells, rules, times) do    IO.write String.duplicate(" ", times)    IO.puts String.replace(cells, "0", ".") |> String.replace("1", "#")    c = not_cell(String.first(cells)) <> cells <> not_cell(String.last(cells))    next_cells = Enum.map_join(0..String.length(cells)+1, fn i ->      Map.get(rules, String.slice(c, i, 3))    end)    each(next_cells, rules, times-1)  end   defp not_cell("0"), do: "11"  defp not_cell("1"), do: "00"   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  endend Enum.each([18, 30], fn rule ->  IO.puts "\nRule : #{rule}"  Elementary_cellular_automaton.infinite("1", rule, 25)end)`
Output:
```Rule : 18
#
#.#
#...#
#.#.#.#
#.......#
#.#.....#.#
#...#...#...#
#.#.#.#.#.#.#.#
#...............#
#.#.............#.#
#...#...........#...#
#.#.#.#.........#.#.#.#
#.......#.......#.......#
#.#.....#.#.....#.#.....#.#
#...#...#...#...#...#...#...#
#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
#...............................#
#.#.............................#.#
#...#...........................#...#
#.#.#.#.........................#.#.#.#
#.......#.......................#.......#
#.#.....#.#.....................#.#.....#.#
#...#...#...#...................#...#...#...#
#.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.#
#...............#...............#...............#

Rule : 30
#
###
##..#
##.####
##..#...#
##.####.###
##..#....#..#
##.####..######
##..#...###.....#
##.####.##..#...###
##..#....#.####.##..#
##.####..##.#....#.####
##..#...###..##..##.#...#
##.####.##..###.###..##.###
##..#....#.###...#..###..#..#
##.####..##.#..#.#####..#######
##..#...###..####.#....###......#
##.####.##..###....##..##..#....###
##..#....#.###..#..##.###.####..##..#
##.####..##.#..######..#...#...###.####
##..#...###..####.....####.###.##...#...#
##.####.##..###...#...##....#...#.#.###.###
##..#....#.###..#.###.##.#..###.##.#.#...#..#
##.####..##.#..###.#...#..####...#..#.##.######
##..#...###..####...##.#####...#.#####.#..#.....#
```

## Go

Translation of: C++
`package main import (    "fmt"    "strings") func btoi(b bool) int {    if b {        return 1    }    return 0} func evolve(l, rule int) {    fmt.Printf(" Rule #%d:\n", rule)    cells := "O"    for x := 0; x < l; x++ {        cells = addNoCells(cells)        width := 40 + (len(cells) >> 1)        fmt.Printf("%*s\n", width, cells)        cells = step(cells, rule)    }} func step(cells string, rule int) string {    newCells := new(strings.Builder)    for i := 0; i < len(cells)-2; i++ {        bin := 0        b := uint(2)        for n := i; n < i+3; n++ {            bin += btoi(cells[n] == 'O') << b            b >>= 1        }        a := '.'        if rule&(1<<uint(bin)) != 0 {            a = 'O'        }        newCells.WriteRune(a)    }    return newCells.String()} func addNoCells(cells string) string {    l, r := "O", "O"    if cells[0] == 'O' {        l = "."    }    if cells[len(cells)-1] == 'O' {        r = "."    }    cells = l + cells + r    cells = l + cells + r    return cells} func main() {    for _, r := range []int{90, 30} {        evolve(25, r)        fmt.Println()    }}`
Output:
``` Rule #90:
..O..
..O.O..
..O...O..
..O.O.O.O..
..O.......O..
..O.O.....O.O..
..O...O...O...O..
..O.O.O.O.O.O.O.O..
..O...............O..
..O.O.............O.O..
..O...O...........O...O..
..O.O.O.O.........O.O.O.O..
..O.......O.......O.......O..
..O.O.....O.O.....O.O.....O.O..
..O...O...O...O...O...O...O...O..
..O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O..
..O...............................O..
..O.O.............................O.O..
..O...O...........................O...O..
..O.O.O.O.........................O.O.O.O..
..O.......O.......................O.......O..
..O.O.....O.O.....................O.O.....O.O..
..O...O...O...O...................O...O...O...O..
..O.O.O.O.O.O.O.O.................O.O.O.O.O.O.O.O..
..O...............O...............O...............O..

Rule #30:
..O..
..OOO..
..OO..O..
..OO.OOOO..
..OO..O...O..
..OO.OOOO.OOO..
..OO..O....O..O..
..OO.OOOO..OOOOOO..
..OO..O...OOO.....O..
..OO.OOOO.OO..O...OOO..
..OO..O....O.OOOO.OO..O..
..OO.OOOO..OO.O....O.OOOO..
..OO..O...OOO..OO..OO.O...O..
..OO.OOOO.OO..OOO.OOO..OO.OOO..
..OO..O....O.OOO...O..OOO..O..O..
..OO.OOOO..OO.O..O.OOOOO..OOOOOOO..
..OO..O...OOO..OOOO.O....OOO......O..
..OO.OOOO.OO..OOO....OO..OO..O....OOO..
..OO..O....O.OOO..O..OO.OOO.OOOO..OO..O..
..OO.OOOO..OO.O..OOOOOO..O...O...OOO.OOOO..
..OO..O...OOO..OOOO.....OOOO.OOO.OO...O...O..
..OO.OOOO.OO..OOO...O...OO....O...O.O.OOO.OOO..
..OO..O....O.OOO..O.OOO.OO.O..OOO.OO.O.O...O..O..
..OO.OOOO..OO.O..OOO.O...O..OOOO...O..O.OO.OOOOOO..
..OO..O...OOO..OOOO...OO.OOOOO...O.OOOOO.O..O.....O..
```

Infinite lists are natural in Haskell, however the task forces us to deal with lists that are infinite in both directions. These structures could be efficiently implemented as a zipper lists. Moreover, zipper lists are instances of magic `Comonad` class, which gives beautifull implementation of cellular automata.

This solution is kinda involved, but it is guaranteed to be total and correct by type checker.

First we provide the datatype, the viewer and constructor:

`{-# LANGUAGE DeriveFunctor #-} import Control.Comonadimport Data.InfList (InfList (..), (+++))import qualified Data.InfList as Inf data Cells a = Cells (InfList a) a (InfList a) deriving Functor view n (Cells l x r) = reverse (Inf.take n l) ++ [x] ++ (Inf.take n r) fromList []     = fromList [0]fromList (x:xs) = let zeros = Inf.repeat 0                  in Cells zeros x (xs +++ zeros)`

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 Cells where  extract (Cells _ x _) = x  duplicate x = Cells (rewind left x) x (rewind right x)    where      rewind dir = Inf.iterate dir . dir      right (Cells l x (r ::: rs)) = Cells (x ::: l) r rs      left  (Cells (l ::: ls) x r) = Cells ls l (x ::: r) runCA rule = iterate (=>> step)  where step (Cells (l ::: _) x (r ::: _)) = rule l x r`

Following is the rule definition and I/O routine:

`rule n l x r = n `div` (2^(4*l + 2*x + r)) `mod` 2 displayCA n w rule init = mapM_ putStrLn \$ take n result  where result = fmap display . view w <\$> runCA rule init        display 0 = ' '        display _ = '*'`
Output:
```λ> displayCA 30 20 (rule 90) (fromList [1])
*
* *
*   *
* * * *
*       *
* *     * *
*   *   *   *
* * * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *
* *     * *     * *     * *
*   *   *   *   *   *   *   *
* * * * * * * * * * * * * * * *
*                               *
* *                             * *
*   *                           *   *
* * * *                         * * * *
*       *                       *       *
*     * *                     * *     *
*   *   *                   *   *   *
* * * * * *                 * * * * * *
*               *
* *             * *
*   *           *   *
* * * *         * * * *
*       *       *       *       *       *
*     * *     * *     * *     * *     * ```

## J

Implementation note: edges are complement of the first and last represented cell, which we define as 1 for the case of an empty numeric list. (So we can represent an infinite space of 0s but not an infinite space of 1s.)

We actually only extend our edges by 9 positions (which is more than sufficient), and then trim everything up to the first change from each edge (so the result from a rule which results in all 1s will be silently converted to an empty all 0s result).

Note however that this means that positions in the result are not anchored to positions in the argument. They might correspond or they might be "off by one" position.

Implementation:

`ext9=: (9#1-{.!.1),],9#1-{:!.1trim=: |[email protected](}.~ ] i. 1-{.)^:2next=: [email protected](((8\$2) #: [) {~ 2 #. 1 - [: |: |.~"1 0&_1 0 1@]) ext9`

In other words, a wrapped version of the original implementation.

example use:

`   ' *'{~90 next^:(i.9) 1*                * *              *   *            * * * *          *       *        * *     * *      *   *   *   *    * * * * * * * *  *               *`

Looks like a Sierpinski triangle

## Kotlin

Translation of: C++
`// version 1.1.51 fun evolve(l: Int, rule: Int) {    println(" Rule #\$rule:")    var cells = StringBuilder("*")    for (x in 0 until l) {        addNoCells(cells)        val width = 40 + (cells.length shr 1)        println(cells.padStart(width))        cells = step(cells, rule)    }} fun step(cells: StringBuilder, rule: Int): StringBuilder {    val newCells = StringBuilder()    for (i in 0 until cells.length - 2) {        var bin = 0        var b = 2        for (n in i until i + 3) {            bin += (if (cells[n] == '*') 1 else 0) shl b            b = b shr 1        }        val a = if ((rule and (1 shl bin)) != 0) '*' else '.'        newCells.append(a)    }    return newCells} fun addNoCells(s: StringBuilder) {    val l = if (s[0] == '*') '.' else '*'    val r = if (s[s.length - 1] == '*') '.' else '*'    repeat(2) {       s.insert(0, l)       s.append(r)    }} fun main(args: Array<String>) {    evolve(35, 90)    println()}`
Output:
``` Rule #90:
..*..
..*.*..
..*...*..
..*.*.*.*..
..*.......*..
..*.*.....*.*..
..*...*...*...*..
..*.*.*.*.*.*.*.*..
..*...............*..
..*.*.............*.*..
..*...*...........*...*..
..*.*.*.*.........*.*.*.*..
..*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................*..
..*.*.............................*.*..
..*...*...........................*...*..
..*.*.*.*.........................*.*.*.*..
..*.......*.......................*.......*..
..*.*.....*.*.....................*.*.....*.*..
..*...*...*...*...................*...*...*...*..
..*.*.*.*.*.*.*.*.................*.*.*.*.*.*.*.*..
..*...............*...............*...............*..
..*.*.............*.*.............*.*.............*.*..
..*...*...........*...*...........*...*...........*...*..
..*.*.*.*.........*.*.*.*.........*.*.*.*.........*.*.*.*..
..*.......*.......*.......*.......*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................................................*..
..*.*.............................................................*.*..
..*...*...........................................................*...*..
```

## Perl

The edges of a pattern is implicitly repeating. The code will try to lineup output by padding up to 40 spaces to the left, but since the cells keep expanding, that has to end somewhere.

`sub evolve {	my (\$rule, \$pattern) = @_;	my \$offset = 0; 	while (1) {		my (\$l, \$r, \$st);		\$pattern =~ s/^((.)\g2*)/\$2\$2/ and \$l = \$2, \$offset -= length(\$2);		\$pattern =~ s/(.)\g1*\$/\$1\$1/   and \$r = \$1; 		\$st = \$pattern; 		\$pattern =~ tr/01/.#/;		printf "%5d| %s%s\n", \$offset, ' ' x (40 + \$offset), \$pattern; 		\$pattern = join '', map(1 & (\$rule>>oct "0b\$_"),				\$l x 3,				map(substr(\$st, \$_, 3), 0 .. length(\$st)-3),				\$r x 3);	}} evolve(90, "010");`
Output:
```   -1|                                        ..#..
-2|                                       ..#.#..
-3|                                      ..#...#..
-4|                                     ..#.#.#.#..
-5|                                    ..#.......#..
-6|                                   ..#.#.....#.#..
-7|                                  ..#...#...#...#..
-8|                                 ..#.#.#.#.#.#.#.#..
-9|                                ..#...............#..
-10|                               ..#.#.............#.#..
-11|                              ..#...#...........#...#..
-12|                             ..#.#.#.#.........#.#.#.#..
-13|                            ..#.......#.......#.......#..
---(infinite more lines snipped)---
```

## Perl 6

This version, while it is capable of working with infinite length cellular automata, makes the assumption that any cells which have not been explicitly examined are in a 'null' state, neither '0' or '1'. Further it makes the assumption that a null cell, on being examined, initially contains nothing (░). Otherwise it would take infinite time to calculate every row and would be exceptionally boring to watch.

Based heavily on the code from the One-dimensional cellular automata task. Example uses rule 90 (Sierpinski triangle).

`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 Automaton \$a .= new: :rule(90), :cells(flat '010'.comb); # display the first 20 rowssay \$a++ for ^20; # then calculate the other infinite number of rows, (may take a while)\$a++ for ^Inf;`
Output:
```░▲░
░▲░▲░
░▲░░░▲░
░▲░▲░▲░▲░
░▲░░░░░░░▲░
░▲░▲░░░░░▲░▲░
░▲░░░▲░░░▲░░░▲░
░▲░▲░▲░▲░▲░▲░▲░▲░
░▲░░░░░░░░░░░░░░░▲░
░▲░▲░░░░░░░░░░░░░▲░▲░
░▲░░░▲░░░░░░░░░░░▲░░░▲░
░▲░▲░▲░▲░░░░░░░░░▲░▲░▲░▲░
░▲░░░░░░░▲░░░░░░░▲░░░░░░░▲░
░▲░▲░░░░░▲░▲░░░░░▲░▲░░░░░▲░▲░
░▲░░░▲░░░▲░░░▲░░░▲░░░▲░░░▲░░░▲░
░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░
░▲░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░▲░
░▲░▲░░░░░░░░░░░░░░░░░░░░░░░░░░░░░▲░▲░
░▲░░░▲░░░░░░░░░░░░░░░░░░░░░░░░░░░▲░░░▲░
░▲░▲░▲░▲░░░░░░░░░░░░░░░░░░░░░░░░░▲░▲░▲░▲░
^C
```

## Python

Infinite generator but only print 25 lines of each rule.

`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 = 25    for rule in (90, 30):        print('\nRule: %i' % rule)        for i, c in zip(range(lines), eca_infinite('1', rule)):            print('%2i: %s%s' % (i, ' '*(lines - i), c.replace('0', '.').replace('1', '#')))`
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:  #...............#...............#...............#

Rule: 30
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:  ##..#...###..####...##.#####...#.#####.#..#.....#```

## Racket

Uses solution to Elementary cellular automaton saved in file "Elementary_cellular_automata.rkt"

`#lang racket; below is the code from the parent task(require "Elementary_cellular_automata.rkt")(require racket/fixnum) (define (wrap-rule-infinite v-in vl-1 offset)  (define l-bit-set? (bitwise-bit-set? (fxvector-ref v-in 0) usable-bits/fixnum-1))  (define r-bit-set? (bitwise-bit-set? (fxvector-ref v-in vl-1) 0))  ;; if we need to extend left offset is reduced by 1  (define l-pad-words (if l-bit-set? 1 0))  (define r-pad-words (if r-bit-set? 1 0))  (define new-words (fx+ l-pad-words r-pad-words))  (cond    [(fx= 0 new-words) (values v-in vl-1 offset)] ; nothing changes    [else     (define offset- (if l-bit-set? (fx- offset 1) offset))     (define l-sequence (if l-bit-set? (in-value 0) (in-sequences)))     (define vl-1+ (fx+ vl-1 (fx+ l-pad-words r-pad-words)))       (define v-out       (for/fxvector           #:length (fx+ vl-1+ 1) #:fill 0 ; right padding           ([f (in-sequences l-sequence (in-fxvector v-in))])        f))     (values v-out vl-1+ offset-)])) (module+ main  (define ng/90/infinite (CA-next-generation 90 #:wrap-rule wrap-rule-infinite))  (for/fold ([v (fxvector #b10000000000000000000)]             [o 1]) ; start by pushing output right by one            ([step (in-range 40)])    (show-automaton v #:step step #:push-right o)    (newline)    (ng/90/infinite v o)))`
Output:
```[         0] ..............................000000000010000000000000000000
[         1] ..............................000000000101000000000000000000
[         2] ..............................000000001000100000000000000000
[         3] ..............................000000010101010000000000000000
[         4] ..............................000000100000001000000000000000
[         5] ..............................000001010000010100000000000000
[         6] ..............................000010001000100010000000000000
[         7] ..............................000101010101010101000000000000
[         8] ..............................001000000000000000100000000000
[         9] ..............................010100000000000001010000000000
[        10] ..............................100010000000000010001000000000
[        11] 000000000000000000000000000001010101000000000101010100000000
[        12] 000000000000000000000000000010000000100000001000000010000000
[        13] 000000000000000000000000000101000001010000010100000101000000
[        14] 000000000000000000000000001000100010001000100010001000100000
[        15] 000000000000000000000000010101010101010101010101010101010000
[        16] 000000000000000000000000100000000000000000000000000000001000
[        17] 000000000000000000000001010000000000000000000000000000010100
[        18] 000000000000000000000010001000000000000000000000000000100010
[        19] 000000000000000000000101010100000000000000000000000001010101
[        20] 000000000000000000001000000010000000000000000000000010000000100000000000000000000000000000
[        21] 000000000000000000010100000101000000000000000000000101000001010000000000000000000000000000
[        22] 000000000000000000100010001000100000000000000000001000100010001000000000000000000000000000
[        23] 000000000000000001010101010101010000000000000000010101010101010100000000000000000000000000
[        24] 000000000000000010000000000000001000000000000000100000000000000010000000000000000000000000
[        25] 000000000000000101000000000000010100000000000001010000000000000101000000000000000000000000
[        26] 000000000000001000100000000000100010000000000010001000000000001000100000000000000000000000
[        27] 000000000000010101010000000001010101000000000101010100000000010101010000000000000000000000
[        28] 000000000000100000001000000010000000100000001000000010000000100000001000000000000000000000
[        29] 000000000001010000010100000101000001010000010100000101000001010000010100000000000000000000
[        30] 000000000010001000100010001000100010001000100010001000100010001000100010000000000000000000
[        31] 000000000101010101010101010101010101010101010101010101010101010101010101000000000000000000
[        32] 000000001000000000000000000000000000000000000000000000000000000000000000100000000000000000
[        33] 000000010100000000000000000000000000000000000000000000000000000000000001010000000000000000
[        34] 000000100010000000000000000000000000000000000000000000000000000000000010001000000000000000
[        35] 000001010101000000000000000000000000000000000000000000000000000000000101010100000000000000
[        36] 000010000000100000000000000000000000000000000000000000000000000000001000000010000000000000
[        37] 000101000001010000000000000000000000000000000000000000000000000000010100000101000000000000
[        38] 001000100010001000000000000000000000000000000000000000000000000000100010001000100000000000
[        39] 010101010101010100000000000000000000000000000000000000000000000001010101010101010000000000
#fx(536879104 0 33554944)
0```

## Ruby

Translation of: Python
`def notcell(c)  c.tr('01','10')end def eca_infinite(cells, rule)  neighbours2next = Hash[8.times.map{|i|["%03b"%i, "01"[rule[i]]]}]  c = cells  Enumerator.new do |y|    loop do      y << c      c = notcell(c[0])*2 + c + notcell(c[-1])*2        # Extend and pad the ends      c = (1..c.size-2).map{|i| neighbours2next[c[i-1..i+1]]}.join    end  endend if __FILE__ == \$0  lines = 25  for rule in [90, 30]    puts "\nRule: %i" % rule    for i, c in (0...lines).zip(eca_infinite('1', rule))      puts '%2i: %s%s' % [i, ' '*(lines - i), c.tr('01', '.#')]    end  endend`

The output is the same as the Python entry.

## Sidef

Translation of: Perl
`func evolve(rule, bin) {    var offset = 0    var (l='', r='')    Inf.times {        bin.sub!(/^((.)\g2*)/, {|_s1, s2| l = s2; offset -= s2.len; s2*2 })        bin.sub!(/(.)\g1*\$/, {|s1| r = s1; s1*2 })        printf("%5d| %s%s\n", offset, ' ' * (40 + offset), bin.tr('01','.#'))        bin = [l*3, 0.to(bin.len-3).map{|i| bin.substr(i, 3) }..., r*3 ].map { |t|                1 & (rule >> t.bin)        }.join    }} evolve(90, "010")`
Output:
```   -1|                                        ..#..
-2|                                       ..#.#..
-3|                                      ..#...#..
-4|                                     ..#.#.#.#..
-5|                                    ..#.......#..
-6|                                   ..#.#.....#.#..
-7|                                  ..#...#...#...#..
-8|                                 ..#.#.#.#.#.#.#.#..
-9|                                ..#...............#..
-10|                               ..#.#.............#.#..
-11|                              ..#...#...........#...#..
-12|                             ..#.#.#.#.........#.#.#.#..
-13|                            ..#.......#.......#.......#..
-14|                           ..#.#.....#.#.....#.#.....#.#..
-15|                          ..#...#...#...#...#...#...#...#..
-16|                         ..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..
-17|                        ..#...............................#..
-18|                       ..#.#.............................#.#..
-19|                      ..#...#...........................#...#..
-20|                     ..#.#.#.#.........................#.#.#.#..
⋮
```

## Tcl

Works with: Tcl version 8.6
`package require Tcl 8.6 oo::class create InfiniteElementaryAutomaton {    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 {left state right} {	set state [list \$left {*}\$state \$right]	set len [llength \$state]	for {set i -1;set j 0;set k 1} {\$j < \$len} {incr i;incr j;incr k} {	    set a [expr {\$i<0 ? \$left : [lindex \$state \$i]}]	    set b [lindex \$state \$j]	    set c [expr {\$k==\$len ? \$right : [lindex \$state \$k]}]	    lappend result [dict get \$rules \$a\$b\$c]	}	return \$result    }     method evolveEnd {endState} {	return [dict get \$rules \$endState\$endState\$endState]    }     # Simple driver method; omit the initial state to get a centred dot    method run {steps {initialState "010"}} {	set cap [string repeat "\u2026" \$steps]	set s [split [string map ". 0 # 1" \$initialState] ""]	set left [lindex \$s 0]	set right [lindex \$s end]	set s [lrange \$s 1 end-1]	for {set i 0} {\$i < \$steps} {incr i} {	    puts \$cap[string map "0 . 1 #" \$left[join \$s ""]\$right]\$cap	    set s [my evolve \$left \$s \$right]	    set left [my evolveEnd \$left]	    set right [my evolveEnd \$right]	    set cap [string range \$cap 1 end]	}	puts \$cap[string map "0 . 1 #" \$left[join \$s ""]\$right]\$cap    }} foreach num {90 30} {    puts "Rule \${num}:"    set rule [InfiniteElementaryAutomaton new \$num]    \$rule run 25    \$rule destroy}`
Output:
```Rule 90:
………………………………………………………………….#.…………………………………………………………………
……………………………………………………………….#.#.………………………………………………………………
…………………………………………………………….#...#.……………………………………………………………
………………………………………………………….#.#.#.#.…………………………………………………………
……………………………………………………….#.......#.………………………………………………………
…………………………………………………….#.#.....#.#.……………………………………………………
………………………………………………….#...#...#...#.…………………………………………………
……………………………………………….#.#.#.#.#.#.#.#.………………………………………………
…………………………………………….#...............#.……………………………………………
………………………………………….#.#.............#.#.…………………………………………
……………………………………….#...#...........#...#.………………………………………
…………………………………….#.#.#.#.........#.#.#.#.……………………………………
………………………………….#.......#.......#.......#.…………………………………
……………………………….#.#.....#.#.....#.#.....#.#.………………………………
…………………………….#...#...#...#...#...#...#...#.……………………………
………………………….#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.…………………………
……………………….#...............................#.………………………
…………………….#.#.............................#.#.……………………
………………….#...#...........................#...#.…………………
……………….#.#.#.#.........................#.#.#.#.………………
…………….#.......#.......................#.......#.……………
………….#.#.....#.#.....................#.#.....#.#.…………
……….#...#...#...#...................#...#...#...#.………
…….#.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.#.……
….#...............#...............#...............#.…
.#.#.............#.#.............#.#.............#.#.
Rule 30:
………………………………………………………………….#.…………………………………………………………………
……………………………………………………………….###.………………………………………………………………
…………………………………………………………….##..#.……………………………………………………………
………………………………………………………….##.####.…………………………………………………………
……………………………………………………….##..#...#.………………………………………………………
…………………………………………………….##.####.###.……………………………………………………
………………………………………………….##..#....#..#.…………………………………………………
……………………………………………….##.####..######.………………………………………………
…………………………………………….##..#...###.....#.……………………………………………
………………………………………….##.####.##..#...###.…………………………………………
……………………………………….##..#....#.####.##..#.………………………………………
…………………………………….##.####..##.#....#.####.……………………………………
………………………………….##..#...###..##..##.#...#.…………………………………
……………………………….##.####.##..###.###..##.###.………………………………
…………………………….##..#....#.###...#..###..#..#.……………………………
………………………….##.####..##.#..#.#####..#######.…………………………
……………………….##..#...###..####.#....###......#.………………………
…………………….##.####.##..###....##..##..#....###.……………………
………………….##..#....#.###..#..##.###.####..##..#.…………………
……………….##.####..##.#..######..#...#...###.####.………………
…………….##..#...###..####.....####.###.##...#...#.……………
………….##.####.##..###...#...##....#...#.#.###.###.…………
……….##..#....#.###..#.###.##.#..###.##.#.#...#..#.………
…….##.####..##.#..###.#...#..####...#..#.##.######.……
….##..#...###..####...##.#####...#.#####.#..#.....#.…
.##.####.##..###...#.##..#....#.##.#.....#####...###.
```

## zkl

Translation of: D
`nLines,flipCell := 25, fcn(c){ (c=="1") and "0" or "1" };foreach rule in (T(90,30)){   println("\nRule: ", rule);   ruleBits:="%08.2B".fmt(rule);  // eg 90-->"01011010"   neighs2next:=(8).pump(Dictionary(),      'wrap(n){ T("%03.2B".fmt(n), ruleBits.reverse()[n]) });   C:="1";  // C is "1"s and "0"s, I'll auto cast to Int as needed   foreach i in (nLines){      println("%2d: %s%s".fmt(i," "*(nLines - i), C.translate("01",".#")));      C=String(flipCell(C[0])*2, C, flipCell(C[-1])*2);      C=[1..C.len()-2].pump(String,'wrap(n){ neighs2next[C[n-1,3]] });   }}`
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:  #...............#...............#...............#

Rule: 30
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:  ##..#...###..####...##.#####...#.#####.#..#.....#
```