Elementary cellular automaton/Infinite length: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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Uses 0-expansion either side |
Uses 0-expansion either side |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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t=s, r = "........" |
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<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">".#."</span><span style="color: #0000FF;">,</span> |
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integer rule = 18, k, l = length(s), w = 0 |
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<span style="color: #000000;">t</span><span style="color: #0000FF;">=</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"........"</span> |
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for i=1 to 8 do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">rule</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
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r[i] = iff(mod(rule,2)?'#':'.') |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span> |
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rule = floor(rule/2) |
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<span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rule</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)?</span><span style="color: #008000;">'#'</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'.'</span><span style="color: #0000FF;">)</span> |
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end for |
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<span style="color: #000000;">rule</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rule</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> |
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for i=0 to 25 do |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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?repeat(' ',floor((55-length(s))/2))&s |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">25</span> <span style="color: #008080;">do</span> |
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for j=1 to l do |
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">55</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))&</span><span style="color: #000000;">s</span> |
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k = (s[iff(j=1?l:j-1)]='#')*4 |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span> |
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+ (s[ j ]='#')*2 |
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<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #000000;">l</span><span style="color: #0000FF;">:</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)]=</span><span style="color: #008000;">'#'</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">4</span> |
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+ (s[iff(j=l?1:j+1)]='#')+1 |
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<span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">]=</span><span style="color: #008000;">'#'</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">2</span> |
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t[j] = r[k] |
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<span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span><span style="color: #0000FF;">?</span><span style="color: #000000;">1</span><span style="color: #0000FF;">:</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)]=</span><span style="color: #008000;">'#'</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span> |
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end for |
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<span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> |
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if t[1]='#' then t = '.'&t end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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if t[$]='#' then t = t&'.' end if |
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<span style="color: #008080;">if</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'#'</span> <span style="color: #008080;">then</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'.'</span><span style="color: #0000FF;">&</span><span style="color: #000000;">t</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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l = length(t) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[$]=</span><span style="color: #008000;">'#'</span> <span style="color: #008080;">then</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">&</span><span style="color: #008000;">'.'</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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s = t |
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<span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> |
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| ⚫ | |||
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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| ⚫ | |||
{{out}} |
{{out}} |
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<pre> |
<pre> |
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Revision as of 01:10, 14 January 2022
You are encouraged to solve this task according to the task description, using any language you may know.
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.
11l
<lang 11l>F step(cells, rule)
V result = ‘’
L(i) 0 .< cells.len - 2
V bin = 0
V b = 2
L(n) i .< i + 3
bin += Int(cells[n] == ‘*’) << b
b >>= 1
V a = I (rule [&] (1 << bin)) != 0 {‘*’} E ‘.’
result ‘’= a
R result
F addNoCells(&cells)
V left = I cells[0] == ‘*’ {‘.’} E ‘*’
V right = I cells.last == ‘*’ {‘.’} E ‘*’
cells = left‘’cells‘’right
cells = left‘’cells‘’right
F evolve(limit, rule)
print(‘Rule #’rule)
V cells = ‘*’
L 0 .< limit
addNoCells(&cells)
V width = 40 + (cells.len >> 1)
print(cells.rjust(width))
cells = step(cells, rule)
evolve(35, 90)</lang>
- Output:
Rule #90
..*..
..*.*..
..*...*..
..*.*.*.*..
..*.......*..
..*.*.....*.*..
..*...*...*...*..
..*.*.*.*.*.*.*.*..
..*...............*..
..*.*.............*.*..
..*...*...........*...*..
..*.*.*.*.........*.*.*.*..
..*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................*..
..*.*.............................*.*..
..*...*...........................*...*..
..*.*.*.*.........................*.*.*.*..
..*.......*.......................*.......*..
..*.*.....*.*.....................*.*.....*.*..
..*...*...*...*...................*...*...*...*..
..*.*.*.*.*.*.*.*.................*.*.*.*.*.*.*.*..
..*...............*...............*...............*..
..*.*.............*.*.............*.*.............*.*..
..*...*...........*...*...........*...*...........*...*..
..*.*.*.*.........*.*.*.*.........*.*.*.*.........*.*.*.*..
..*.......*.......*.......*.......*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................................................*..
..*.*.............................................................*.*..
..*...*...........................................................*...*..
C++
<lang cpp>
- 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;
} </lang>
- 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
<lang d>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;
}
}
}</lang> The output is the same as the Python entry.
Elixir
<lang elixir> 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
end
end
Enum.each([18, 30], fn rule ->
IO.puts "\nRule : #{rule}"
Elementary_cellular_automaton.infinite("1", rule, 25)
end)</lang>
- Output:
Rule : 18
#
#.#
#...#
#.#.#.#
#.......#
#.#.....#.#
#...#...#...#
#.#.#.#.#.#.#.#
#...............#
#.#.............#.#
#...#...........#...#
#.#.#.#.........#.#.#.#
#.......#.......#.......#
#.#.....#.#.....#.#.....#.#
#...#...#...#...#...#...#...#
#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
#...............................#
#.#.............................#.#
#...#...........................#...#
#.#.#.#.........................#.#.#.#
#.......#.......................#.......#
#.#.....#.#.....................#.#.....#.#
#...#...#...#...................#...#...#...#
#.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.#
#...............#...............#...............#
Rule : 30
#
###
##..#
##.####
##..#...#
##.####.###
##..#....#..#
##.####..######
##..#...###.....#
##.####.##..#...###
##..#....#.####.##..#
##.####..##.#....#.####
##..#...###..##..##.#...#
##.####.##..###.###..##.###
##..#....#.###...#..###..#..#
##.####..##.#..#.#####..#######
##..#...###..####.#....###......#
##.####.##..###....##..##..#....###
##..#....#.###..#..##.###.####..##..#
##.####..##.#..######..#...#...###.####
##..#...###..####.....####.###.##...#...#
##.####.##..###...#...##....#...#.#.###.###
##..#....#.###..#.###.##.#..###.##.#.#...#..#
##.####..##.#..###.#...#..####...#..#.##.######
##..#...###..####...##.#####...#.#####.#..#.....#
Go
<lang go>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()
}
}</lang>
- 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..
Haskell
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:
<lang Haskell>{-# LANGUAGE DeriveFunctor #-}
import Control.Comonad import 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)</lang>
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:
<lang Haskell>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</lang>
Following is the rule definition and I/O routine:
<lang Haskell>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 _ = '*'</lang>
- Output:
λ> displayCA 30 20 (rule 90) (fromList [1])
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * *
* * * * * *
* * * * * * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * * * *
* * * * * * * * * *
See also Elementary cellular automaton#Haskell
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:
<lang J>ext9=: (9#1-{.!.1),],9#1-{:!.1 trim=: |.@(}.~ ] i. 1-{.)^:2 next=: trim@(((8$2) #: [) {~ 2 #. 1 - [: |: |.~"1 0&_1 0 1@]) ext9</lang>
In other words, a wrapped version of the original implementation.
example use:
<lang J> ' *'{~90 next^:(i.9) 1
- *
- *
- * * *
- *
- * * *
- * * *
- * * * * * * *
- *</lang>
Looks like a Sierpinski triangle
jq
Adapted from Python
Works with gojq, the Go implementation of jq
Preliminaries <lang jq> def lpad($len; $fill): tostring | ($len - length) as $l | ($fill * $l)[:$l] + .;
def lpad($len): lpad($len; " ");
- Like *ix `tr` but it is as though $to is padded with blanks
def tr($from;$to):
explode as $s
| ($from | explode) as $f
| ($to | explode) as $t
| reduce range(0;length) as $i ([];
($f | index($s[$i])) as $ix
| if $ix then . + [$t[$ix] // " "]
else . + [$s[$i]]
end )
| implode;
- Input: a non-negative integer
- Output: the corresponding stream of bits (0s and 1s),
- least significant digit first, with a final 0
def stream:
recurse(if . > 0 then ./2|floor else empty end) | . % 2 ;
- input: an array, e.g. as produced by [7|stream]
- output: the corresponding binary string
def to_b: reverse | map(tostring) | join("") | sub("^0";"");</lang> The Cellular Automaton <lang jq># Output: an unbounded stream of the form [count, row]
- giving the rows produced by the eca defined by
- $cells (a string) and $rule (an integer)
def eca_infinite($cells; $rule):
def notcell: tr("01";"10") ;
def rule2hash($rule):
[$rule | stream] as $r
| reduce range(0;8) as $i ({};
. + { ($i|[stream]|to_b|lpad(3;"0")): ($r[$i] // 0)});
rule2hash($rule) as $neighbours2next
| [0, $cells],
foreach range(1; infinite) as $i ({c: $cells};
.c = (.c[0:1]|notcell)*2 + .c + (.c[-1:]|notcell)*2 # Extend and pad the ends
| .c = ([range(1; .c|length - 1) as $i | $neighbours2next[.c[$i-1:$i+2] ]] | join(""));
[$i, .c] ) ;
</lang> The Task <lang jq># $lines specifies the number of lines to display for each eca def main($lines):
(90, 30) as $rule
| "\nRule: \($rule)",
(limit($lines; eca_infinite("1"; $rule)
| .[0] as $line
| ($line|lpad(3)) + " " * ($lines - $line) + (.[1] | tr("01"; ".#") )));
main(25)</lang>
- Output:
As for Python.
Julia
<lang julia>function ecainfinite(cells, rule, n)
notcell(cell) = (cell == '1') ? '0' : '1'
rulebits = reverse(string(rule, base = 2, pad = 8))
neighbors2next = Dict(string(n - 1, base=2, pad=3) => rulebits[n] for n in 1:8)
ret = String[]
for i in 1:n
push!(ret, cells)
cells = notcell(cells[1])^2 * cells * notcell(cells[end])^2 # Extend/pad ends
cells = join([neighbors2next[cells[i:i+2]] for i in 1:length(cells)-2], "")
end
ret
end
function testinfcells(lines::Integer)
for rule in [90, 30]
println("\nRule: $rule ($(string(rule, base = 2, pad = 8)))")
s = ecainfinite("1", rule, lines)
for i in 1:lines
println("$i: ", " "^(lines - i), replace(replace(s[i], "0" => "."), "1" => "#"))
end
end
end
testinfcells(25)
</lang>
- Output:
Rule: 90 (01011010) 1: # 2: #.# 3: #...# 4: #.#.#.# 5: #.......# 6: #.#.....#.# 7: #...#...#...# 8: #.#.#.#.#.#.#.# 9: #...............# 10: #.#.............#.# 11: #...#...........#...# 12: #.#.#.#.........#.#.#.# 13: #.......#.......#.......# 14: #.#.....#.#.....#.#.....#.# 15: #...#...#...#...#...#...#...# 16: #.#.#.#.#.#.#.#.#.#.#.#.#.#.#.# 17: #...............................# 18: #.#.............................#.# 19: #...#...........................#...# 20: #.#.#.#.........................#.#.#.# 21: #.......#.......................#.......# 22: #.#.....#.#.....................#.#.....#.# 23: #...#...#...#...................#...#...#...# 24: #.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.# 25: #...............#...............#...............# Rule: 30 (00011110) 1: # 2: ### 3: ##..# 4: ##.#### 5: ##..#...# 6: ##.####.### 7: ##..#....#..# 8: ##.####..###### 9: ##..#...###.....# 10: ##.####.##..#...### 11: ##..#....#.####.##..# 12: ##.####..##.#....#.#### 13: ##..#...###..##..##.#...# 14: ##.####.##..###.###..##.### 15: ##..#....#.###...#..###..#..# 16: ##.####..##.#..#.#####..####### 17: ##..#...###..####.#....###......# 18: ##.####.##..###....##..##..#....### 19: ##..#....#.###..#..##.###.####..##..# 20: ##.####..##.#..######..#...#...###.#### 21: ##..#...###..####.....####.###.##...#...# 22: ##.####.##..###...#...##....#...#.#.###.### 23: ##..#....#.###..#.###.##.#..###.##.#.#...#..# 24: ##.####..##.#..###.#...#..####...#..#.##.###### 25: ##..#...###..####...##.#####...#.#####.#..#.....#
Kotlin
<lang scala>// version 1.1.51
fun evolve(l: Int, rule: Int) {
println(" Rule #$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()
}</lang>
- Output:
Rule #90:
..*..
..*.*..
..*...*..
..*.*.*.*..
..*.......*..
..*.*.....*.*..
..*...*...*...*..
..*.*.*.*.*.*.*.*..
..*...............*..
..*.*.............*.*..
..*...*...........*...*..
..*.*.*.*.........*.*.*.*..
..*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................*..
..*.*.............................*.*..
..*...*...........................*...*..
..*.*.*.*.........................*.*.*.*..
..*.......*.......................*.......*..
..*.*.....*.*.....................*.*.....*.*..
..*...*...*...*...................*...*...*...*..
..*.*.*.*.*.*.*.*.................*.*.*.*.*.*.*.*..
..*...............*...............*...............*..
..*.*.............*.*.............*.*.............*.*..
..*...*...........*...*...........*...*...........*...*..
..*.*.*.*.........*.*.*.*.........*.*.*.*.........*.*.*.*..
..*.......*.......*.......*.......*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................................................*..
..*.*.............................................................*.*..
..*...*...........................................................*...*..
Mathematica / Wolfram Language
An infinite background is built-in the language: <lang Mathematica>CellularAutomaton[18, {{1}, 0}, 15] // ArrayPlot CellularAutomaton[30, {{1}, 0}, 15] // ArrayPlot</lang>
Nim
<lang Nim>import strutils
func step(cells: string; rule: int): string =
for i in 0..(cells.len - 3):
var bin = 0
var b = 2
for n in i..(i + 2):
inc bin, ord(cells[n] == '*') shl b
b = b shr 1
let a = if (rule and 1 shl bin) != 0: '*' else: '.'
result.add(a)
func addNoCells(cells: var string) =
let left = if cells[0] == '*': "." else: "*" let right = if cells[^1] == '*': "." else: "*" cells.insert(left) cells.add(right) cells.insert(left) cells.add(right)
proc evolve(limit, rule: int) =
echo "Rule #", rule var cells = "*" for _ in 0..<limit: cells.addNoCells() let width = 40 + cells.len shr 1 echo cells.align(width) cells = cells.step(rule)
evolve(35, 90)</lang>
- 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. <lang perl>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), $r x 3); } }
evolve(90, "010");</lang>
- Output:
-1| ..#.. -2| ..#.#.. -3| ..#...#.. -4| ..#.#.#.#.. -5| ..#.......#.. -6| ..#.#.....#.#.. -7| ..#...#...#...#.. -8| ..#.#.#.#.#.#.#.#.. -9| ..#...............#.. -10| ..#.#.............#.#.. -11| ..#...#...........#...#.. -12| ..#.#.#.#.........#.#.#.#.. -13| ..#.......#.......#.......#.. ---(infinite more lines snipped)---
Phix
Uses 0-expansion either side
with javascript_semantics string s = ".#.", t=s, r = "........" integer rule = 18, k, l = length(s), w = 0 for i=1 to 8 do r[i] = iff(mod(rule,2)?'#':'.') rule = floor(rule/2) end for for i=0 to 25 do ?repeat(' ',floor((55-length(s))/2))&s for j=1 to l do k = (s[iff(j=1?l:j-1)]='#')*4 + (s[ j ]='#')*2 + (s[iff(j=l?1:j+1)]='#')+1 t[j] = r[k] end for if t[1]='#' then t = '.'&t end if if t[$]='#' then t = t&'.' end if l = length(t) s = t end for
- Output:
" .#." " .#.#." " .#...#." " .#.#.#.#." " .#.......#." " .#.#.....#.#." " .#...#...#...#." " .#.#.#.#.#.#.#.#." " .#...............#." " .#.#.............#.#." " .#...#...........#...#." " .#.#.#.#.........#.#.#.#." " .#.......#.......#.......#." " .#.#.....#.#.....#.#.....#.#." " .#...#...#...#...#...#...#...#." " .#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." " .#...............................#." " .#.#.............................#.#." " .#...#...........................#...#." " .#.#.#.#.........................#.#.#.#." " .#.......#.......................#.......#." " .#.#.....#.#.....................#.#.....#.#." " .#...#...#...#...................#...#...#...#." " .#.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.#." " .#...............#...............#...............#." " .#.#.............#.#.............#.#.............#.#."
Python
Infinite generator but only print 25 lines of each rule.
<lang python>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', '#')))</lang>
- 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>#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)))</lang>
- 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
Raku
(formerly 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).
<lang perl6>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 rows
say $a++ for ^20;
- then calculate the other infinite number of rows, (may take a while)
$a++ for ^Inf;</lang>
- Output:
░▲░ ░▲░▲░ ░▲░░░▲░ ░▲░▲░▲░▲░ ░▲░░░░░░░▲░ ░▲░▲░░░░░▲░▲░ ░▲░░░▲░░░▲░░░▲░ ░▲░▲░▲░▲░▲░▲░▲░▲░ ░▲░░░░░░░░░░░░░░░▲░ ░▲░▲░░░░░░░░░░░░░▲░▲░ ░▲░░░▲░░░░░░░░░░░▲░░░▲░ ░▲░▲░▲░▲░░░░░░░░░▲░▲░▲░▲░ ░▲░░░░░░░▲░░░░░░░▲░░░░░░░▲░ ░▲░▲░░░░░▲░▲░░░░░▲░▲░░░░░▲░▲░ ░▲░░░▲░░░▲░░░▲░░░▲░░░▲░░░▲░░░▲░ ░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░▲░ ░▲░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░▲░ ░▲░▲░░░░░░░░░░░░░░░░░░░░░░░░░░░░░▲░▲░ ░▲░░░▲░░░░░░░░░░░░░░░░░░░░░░░░░░░▲░░░▲░ ░▲░▲░▲░▲░░░░░░░░░░░░░░░░░░░░░░░░░▲░▲░▲░▲░ ^C
Ruby
<lang ruby>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
end
end
if __FILE__ == $0
lines = 25
for rule in [90, 30]
puts "\nRule: %i" % rule
for i, c in (0...lines).zip(eca_infinite('1', rule))
puts '%2i: %s%s' % [i, ' '*(lines - i), c.tr('01', '.#')]
end
end
end</lang> The output is the same as the Python entry.
Sidef
<lang ruby>func evolve(rule, bin) {
var offset = 0
var (l=, r=)
Inf.times {
bin.sub!(/^((.)\g2*)/, {|_s1, s2| l = s2; offset -= s2.len; s2*2 })
bin.sub!(/(.)\g1*$/, {|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")</lang>
- Output:
-1| ..#.. -2| ..#.#.. -3| ..#...#.. -4| ..#.#.#.#.. -5| ..#.......#.. -6| ..#.#.....#.#.. -7| ..#...#...#...#.. -8| ..#.#.#.#.#.#.#.#.. -9| ..#...............#.. -10| ..#.#.............#.#.. -11| ..#...#...........#...#.. -12| ..#.#.#.#.........#.#.#.#.. -13| ..#.......#.......#.......#.. -14| ..#.#.....#.#.....#.#.....#.#.. -15| ..#...#...#...#...#...#...#...#.. -16| ..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.. -17| ..#...............................#.. -18| ..#.#.............................#.#.. -19| ..#...#...........................#...#.. -20| ..#.#.#.#.........................#.#.#.#.. ⋮
Tcl
<lang tcl>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
}</lang>
- Output:
Rule 90: ………………………………………………………………….#.………………………………………………………………… ……………………………………………………………….#.#.……………………………………………………………… …………………………………………………………….#...#.…………………………………………………………… ………………………………………………………….#.#.#.#.………………………………………………………… ……………………………………………………….#.......#.……………………………………………………… …………………………………………………….#.#.....#.#.…………………………………………………… ………………………………………………….#...#...#...#.………………………………………………… ……………………………………………….#.#.#.#.#.#.#.#.……………………………………………… …………………………………………….#...............#.…………………………………………… ………………………………………….#.#.............#.#.………………………………………… ……………………………………….#...#...........#...#.……………………………………… …………………………………….#.#.#.#.........#.#.#.#.…………………………………… ………………………………….#.......#.......#.......#.………………………………… ……………………………….#.#.....#.#.....#.#.....#.#.……………………………… …………………………….#...#...#...#...#...#...#...#.…………………………… ………………………….#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.………………………… ……………………….#...............................#.……………………… …………………….#.#.............................#.#.…………………… ………………….#...#...........................#...#.………………… ……………….#.#.#.#.........................#.#.#.#.……………… …………….#.......#.......................#.......#.…………… ………….#.#.....#.#.....................#.#.....#.#.………… ……….#...#...#...#...................#...#...#...#.……… …….#.#.#.#.#.#.#.#.................#.#.#.#.#.#.#.#.…… ….#...............#...............#...............#.… .#.#.............#.#.............#.#.............#.#. Rule 30: ………………………………………………………………….#.………………………………………………………………… ……………………………………………………………….###.……………………………………………………………… …………………………………………………………….##..#.…………………………………………………………… ………………………………………………………….##.####.………………………………………………………… ……………………………………………………….##..#...#.……………………………………………………… …………………………………………………….##.####.###.…………………………………………………… ………………………………………………….##..#....#..#.………………………………………………… ……………………………………………….##.####..######.……………………………………………… …………………………………………….##..#...###.....#.…………………………………………… ………………………………………….##.####.##..#...###.………………………………………… ……………………………………….##..#....#.####.##..#.……………………………………… …………………………………….##.####..##.#....#.####.…………………………………… ………………………………….##..#...###..##..##.#...#.………………………………… ……………………………….##.####.##..###.###..##.###.……………………………… …………………………….##..#....#.###...#..###..#..#.…………………………… ………………………….##.####..##.#..#.#####..#######.………………………… ……………………….##..#...###..####.#....###......#.……………………… …………………….##.####.##..###....##..##..#....###.…………………… ………………….##..#....#.###..#..##.###.####..##..#.………………… ……………….##.####..##.#..######..#...#...###.####.……………… …………….##..#...###..####.....####.###.##...#...#.…………… ………….##.####.##..###...#...##....#...#.#.###.###.………… ……….##..#....#.###..#.###.##.#..###.##.#.#...#..#.……… …….##.####..##.#..###.#...#..####...#..#.##.######.…… ….##..#...###..####...##.#####...#.#####.#..#.....#.… .##.####.##..###...#.##..#....#.##.#.....#####...###.
Wren
<lang ecmascript>import "/fmt" for Fmt
var addNoCells = Fn.new { |s|
var l = (s[0] == "*") ? "." : "*"
var r = (s[-1] == "*") ? "." : "*"
for (i in 0..1) {
s.insert(0, l)
s.add(r)
}
}
var step = Fn.new { |cells, rule|
var newCells = []
for (i in 0...cells.count - 2) {
var bin = 0
var b = 2
for (n in i...i + 3) {
bin = bin + (((cells[n] == "*") ? 1 : 0) << b)
b = b >> 1
}
var a = ((rule & (1 << bin)) != 0) ? "*" : "."
newCells.add(a)
}
return newCells
}
var evolve = Fn.new { |l, rule|
System.print(" Rule #%(rule):")
var cells = ["*"]
for (x in 0...l) {
addNoCells.call(cells)
var width = 40 + (cells.count >> 1)
Fmt.print("$*s", width, cells.join())
cells = step.call(cells, rule)
}
}
evolve.call(35, 90) System.print()</lang>
- Output:
Rule #90:
..*..
..*.*..
..*...*..
..*.*.*.*..
..*.......*..
..*.*.....*.*..
..*...*...*...*..
..*.*.*.*.*.*.*.*..
..*...............*..
..*.*.............*.*..
..*...*...........*...*..
..*.*.*.*.........*.*.*.*..
..*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................*..
..*.*.............................*.*..
..*...*...........................*...*..
..*.*.*.*.........................*.*.*.*..
..*.......*.......................*.......*..
..*.*.....*.*.....................*.*.....*.*..
..*...*...*...*...................*...*...*...*..
..*.*.*.*.*.*.*.*.................*.*.*.*.*.*.*.*..
..*...............*...............*...............*..
..*.*.............*.*.............*.*.............*.*..
..*...*...........*...*...........*...*...........*...*..
..*.*.*.*.........*.*.*.*.........*.*.*.*.........*.*.*.*..
..*.......*.......*.......*.......*.......*.......*.......*..
..*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*.....*.*..
..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*...*..
..*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*..
..*...............................................................*..
..*.*.............................................................*.*..
..*...*...........................................................*...*..
zkl
<lang zkl>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]] });
}
}</lang>
- 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: ##..#...###..####...##.#####...#.#####.#..#.....#