Elementary cellular automaton/Random number generator

Rule 30 is considered to be chaotic enough to generate good pseudo-random numbers. As a matter of fact, rule 30 is used by the Mathematica software for its default random number generator.

Task
Elementary cellular automaton/Random number generator
You are encouraged to solve this task according to the task description, using any language you may know.

Steven Wolfram's recommendation for random number generation from rule 30 consists in extracting successive bits in a fixed position in the array of cells, as the automaton changes state.

The purpose of this task is to demonstrate this. With the code written in the parent task, which you don't need to re-write here, show the ten first bytes that emerge from this recommendation. To be precise, you will start with a state of all cells but one equal to zero, and you'll follow the evolution of the particular cell whose state was initially one. Then you'll regroup those bits by packets of eight, reconstituting bytes with the first bit being the most significant.

You can pick which ever length you want for the initial array but it should be visible in the code so that your output can be reproduced with an other language.

For extra-credits, you will make this algorithm run as fast as possible in your language, for instance with an extensive use of bitwise logic.

Reference


11lEdit

Translation of: Nim
V n = 64

F pow2(x)
   R UInt64(1) << x

F evolve(UInt64 =state; rule)
   L 10
      V b = UInt64(0)
      L(q) (7 .. 0).step(-1)
         V st = state
         b [|]= (st [&] 1) << q
         state = 0
         L(i) 0 .< :n
            V t = ((st >> (i - 1)) [|] (st << (:n + 1 - i))) [&] 7
            I (rule [&] pow2(t)) != 0
               state [|]= pow2(i)
      print(‘ ’b, end' ‘’)
   print()

evolve(1, 30)
Output:
 220 197 147 174 117 97 149 171 100 151

CEdit

64-bits array size, cyclic borders.

#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, p, q, b;

	for (p = 0; p < 10; p++) {
		for (b = 0, q = 8; q--; ) {
			ull st = state;
			b |= (st&1) << q;

			for (state = i = 0; i < N; i++)
				if (rule & B(7 & (st>>(i-1) | st<<(N+1-i))))
					state |= B(i);
		}
		printf(" %d", b);
	}
	putchar('\n');
	return;
}

int main(void)
{
	evolve(1, 30);
	return 0;
}
Output:
 220 197 147 174 117 97 149 171 100 151

C++Edit

We'll re-write the code of the parent task here.

#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");
}
unsigned char byte(std::bitset<SIZE> &s) {
    unsigned char b = 0;
    int i;
    for (i=8; i--; ) {
	b |= s[0] << i; 
	evolve(s);
    }
    return b;
}

int main() {
    int i;
    std::bitset<SIZE> state(1);
    for (i=10; i--; )
	printf("%u%c", byte(state), i ? ' ' : '\n');
    return 0;
}
Output:
220 197 147 174 117 97 149 171 240 241

DEdit

Translation of: C

Adapted from the C version, with improvements and bug fixes. Optimized for performance as requested in the task description. This is a lazy range.

import std.stdio, std.range, std.typecons;

struct CellularRNG {
    private uint current;
    private immutable uint rule;
    private ulong state;

    this(in ulong state_, in uint rule_) pure nothrow @safe @nogc {
        this.state = state_;
        this.rule = rule_;
        popFront;
    }

    public enum bool empty = false;
    @property uint front() pure nothrow @safe @nogc { return current; }

    void popFront() pure nothrow @safe @nogc {
        enum uint nBit = 8;
        enum uint NU = ulong.sizeof * nBit;
        current = 0;

        foreach_reverse (immutable i; 0 .. nBit) {
            immutable state2 = state;
            current |= (state2 & 1) << i;

            state = 0;
            /*static*/ foreach (immutable j; staticIota!(0, NU)) {
                // To avoid undefined behavior with out-of-range shifts.
                static if (j > 0)
                    immutable aux1 = state2 >> (j - 1);
                else
                    immutable aux1 = state2 >> 63;

                static if (j == 0)
                    immutable aux2 = state2 << 1;
                else static if (j == 1)
                    immutable aux2 = state2 << 63;
                else
                    immutable aux2 = state2 << (NU + 1 - j);

                immutable aux = 7 & (aux1 | aux2);
                if (rule & (1UL << aux))
                    state |= 1UL << j;
            }
        }
    }
}

void main() {
    CellularRNG(1, 30).take(10).writeln;
    CellularRNG(1, 30).drop(2_000_000).front.writeln;
}
Output:
[220, 197, 147, 174, 117, 97, 149, 171, 100, 151]
44

Run-time: less than two seconds with the ldc2 compiler.

F#Edit

This task uses Elementary cellular automaton#The_Function

// Generate random numbers using Rule 30. Nigel Galloway: August 1st., 2019
eca 30 [|yield 1; yield! Array.zeroCreate 99|]|>Seq.chunkBySize 8|>Seq.map(fun n->n|>Array.mapi(fun n g->g.[0]<<<(7-n))|>Array.sum)|>Seq.take 10|>Seq.iter(printf "%d "); printfn ""
Output:
220 197 147 174 117 97 149 171 240 241

GoEdit

Translation of: C
package main

import "fmt"

const n = 64

func pow2(x uint) uint64 {
    return uint64(1) << x
}

func evolve(state uint64, rule int) {
    for p := 0; p < 10; p++ {
        b := uint64(0)
        for q := 7; q >= 0; q-- {
            st := state
            b |= (st & 1) << uint(q)
            state = 0
            for i := uint(0); i < n; i++ {
                var t1, t2, t3 uint64
                if i > 0 {
                    t1 = st >> (i - 1)
                } else {
                    t1 = st >> 63
                }
                if i == 0 {
                    t2 = st << 1
                } else if i == 1 {
                    t2 = st << 63

                } else {
                    t2 = st << (n + 1 - i)
                }
                t3 = 7 & (t1 | t2)
                if (uint64(rule) & pow2(uint(t3))) != 0 {
                    state |= pow2(i)
                }
            }
        }
        fmt.Printf("%d ", b)
    }
    fmt.Println()
}

func main() {
    evolve(1, 30)
}
Output:
220 197 147 174 117 97 149 171 100 151 

HaskellEdit

Assume the comonadic solution given at Elementary cellular automaton#Haskell is packed in a module CellularAutomata

import CellularAutomata (fromList, rule, runCA)
import Control.Comonad
import Data.List (unfoldr)

rnd = fromBits <$> unfoldr (pure . splitAt 8) bits
  where
    size = 80
    bits =
      extract
        <$> runCA
          (rule 30)
          (fromList (1 : replicate size 0))

fromBits = foldl ((+) . (2 *)) 0
Output:
λ> take 10 rnd
[220,197,147,174,117,97,149,171,240,241]

Using the rule 30 CA it is possible to determine the RandomGen instance which could be utilized by the Random class:

import System.Random

instance RandomGen (Cycle Int) where
  next c =
    let x = c =>> step (rule 30)
     in (fromBits (view x), x)
  split = (,) <*> (fromList . reverse . view)
λ> let r30 = fromList [1,0,1,0,1,0,1,0,1,0,1,0,1] :: Cycle Int

λ> take 15 $ randoms r30
[7509,4949,2517,2229,2365,2067,6753,5662,5609,7576,2885,3017,2912,5081,2356]

λ> take 30 $ randomRs ('A','J') r30
"DHJHHFJHBDDFCBHACHDEHDHFBAEJFE"

We can compare it with standard generator on a small integer range, using simple bin counter:

λ> let bins lst = [ (n, length (filter (==n) lst)) | n <- nub lst]

λ> bins . take 10000 . randomRs ('A','J') $ r30
[('D',1098),('H',1097),('J',1093),('F',850),('B',848),('C',1014),('A',1012),('E',1011),('G',1253),('I',724)]

λ> bins . take 10000 . randomRs ('A','J') <$> getStdGen
[('G',975),('B',1035),('F',970),('J',1034),('I',956),('H',984),('C',1009),('E',1023),('A',1009),('D',1005)]

JEdit

ca is a cellular automata class. The rng class inherits ca and extends it with bit and byte verbs to sample the ca.

coclass'ca'
DOC =: 'locale creation: (RULE ; INITIAL_STATE) conew ''ca'''
create =: 3 :'''RULE STATE'' =: y'
next =: 3 :'STATE =: RULE (((8$2) #: [) {~ [: #. [: -. [: |: |.~"1 0&_1 0 1@]) STATE'
coclass'base'

coclass'rng'
coinsert'ca'
bit =: 3 :'([ next) ({. STATE)'
byte =: [: #. [: , [: bit"0 (i.8)"_
coclass'base'

Having installed these into a j session we create and use the mathematica prng.

                    
   m =: (30 ; 64 {. 1) conew 'rng'
   byte__m"0 i.10
220 197 147 174 117 97 149 171 100 151

JuliaEdit

Translation of: C, Go
function evolve(state, rule, N=64)
    B(x) = UInt64(1) << x
    for p in 0:9
        b = UInt64(0)
        for q in 7:-1:0
            st = UInt64(state)
            b |= (st & 1) << q
            state = UInt64(0)
            for i in 0:N-1
                t1 = (i > 0) ? st >> (i - 1) : st >> (N - 1)
                t2 = (i == 0) ? st << 1 : (i == 1) ? st << (N - 1) : st << (N + 1 - i)
                if UInt64(rule) & B(7 & (t1 | t2)) != 0
                    state |= B(i)
                end
            end
        end
        print("$b ")
    end
    println()
end

evolve(1, 30)
Output:
220 197 147 174 117 97 149 171 100 151

KotlinEdit

Translation of: C
// version 1.1.51

const val N = 64

fun pow2(x: Int) = 1L shl x

fun evolve(state: Long, rule: Int) {
    var state2 = state
    for (p in 0..9) {
        var b = 0
        for (q in 7 downTo 0) {
            val st = state2
            b = (b.toLong() or ((st and 1L) shl q)).toInt()
            state2 = 0L
            for (i in 0 until N) {
                val t = ((st ushr (i - 1)) or (st shl (N + 1 - i)) and 7L).toInt()
                if ((rule.toLong() and pow2(t)) != 0L) state2 = state2 or pow2(i)
            }
        }
        print(" $b")
    }
    println()
}

fun main(args: Array<String>) {
    evolve(1, 30)
}
Output:
 220 197 147 174 117 97 149 171 100 151

Mathematica / Wolfram LanguageEdit

FromDigits[#, 2] & /@ Partition[Flatten[CellularAutomaton[30, {{1}, 0}, {200, 0}]], 8]
Output:
{220, 197, 147, 174, 117, 97, 149, 171, 240, 241, 92, 18, 199, 27, 104, 8, 251, 167, 29, 112, 100, 103, 159, 129, 253}

NimEdit

Translation of: Kotlin
const N = 64

template pow2(x: uint): uint = 1u shl x

proc evolve(state: uint; rule: Positive) =
  var state = state
  for _ in 1..10:
    var b = 0u
    for q in countdown(7, 0):
      let st = state
      b = b or (st and 1) shl q
      state = 0
      for i in 0u..<N:
        let t = (st shr (i - 1) or st shl (N + 1 - i)) and 7
        if (rule.uint and pow2(t)) != 0: state = state or pow2(i)
    stdout.write ' ', b
  echo ""

evolve(1, 30)
Output:
 220 197 147 174 117 97 149 171 100 151

PascalEdit

Works with: Free Pascal

Using ROR and ROL is as fast as assembler and more portable.
Try it online! counting CPU-Cycles 32 vs 31 on Ryzen Zen1 per Byte -> 100Mb/s

Program Rule30;
//http://en.wikipedia.org/wiki/Next_State_Rule_30;
//http://mathworld.wolfram.com/Rule30.html
{$IFDEF FPC}
  {$Mode Delphi}{$ASMMODE INTEL}
  {$OPTIMIZATION ON,ALL}
//  {$CODEALIGN proc=1}
{$ELSE}
  {$APPTYPE CONSOLE}
{$ENDIF}
uses
  SysUtils;
const
  maxRounds = 2*1000*1000;
  rounds    = 10;

var
  Rule30_State : Uint64;

function GetCPU_Time: int64;
type
  TCpu = record
            HiCpu,
            LoCpu : Dword;
         end;
var
  Cput : TCpu;
begin
  asm
  RDTSC;
  MOV Dword Ptr [CpuT.LoCpu],EAX
  MOV Dword Ptr [CpuT.HiCpu],EDX
  end;
  with Cput do
    result := int64(HiCPU) shl 32 + LoCpu;
end;

procedure InitRule30_State;inline;
begin
  Rule30_State:= 1;
end;

procedure Next_State_Rule_30;inline;
var
  run, prev,next: Uint64;
begin
  run  := Rule30_State;
  Prev := RORQword(run,1);
  next := ROLQword(run,1);
  Rule30_State  := (next OR run) XOR prev;
end;

function NextRule30Byte:NativeInt;
//64-BIT can use many registers
//32-Bit still fast
var
  run, prev,next: Uint64;
  myOne : UInt64;
Begin
  run  := Rule30_State;
  result := 0;
  myOne  := 1;
  //Unrolling and inlining Next_State_Rule_30 by hand
  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  run  := (next OR run) XOR prev;

  result := (result+result) OR (run AND myOne);
  next := ROLQword(run,1);
  Prev := RORQword(run,1);
  Rule30_State := (next OR run) XOR prev;
end;

procedure Speedtest;
var
  T1,T0 : INt64;
  i: NativeInt;
Begin
  writeln('Speedtest for statesize of ',64,' bits');
  //Warm up start to wake up CPU takes some time
  For i := 100*1000*1000-1 downto 0 do
    Next_State_Rule_30;

  T0 := GetCPU_Time;
  InitRule30_State;
  For  i := maxRounds-1 downto 0 do
    NextRule30Byte;
  T1 := GetCPU_Time;
  writeln(NextRule30Byte);
  writeln('cycles per Byte : ',(T1-t0)/maxRounds:0:2);
  writeln;
end;

procedure Task;
var
  i: integer;
Begin
  writeln('The task ');
  InitRule30_State;
  For  i := 1 to rounds do
    write(NextRule30Byte:4);
  writeln;
end;

Begin
  SpeedTest;
  Task;
  write(' <ENTER> ');readln;
end.
Output:
//compiled 64-Bit
Speedtest for statesize of 64 bits
44
cycles per Byte : 30.95

The task
 220 197 147 174 117  97 149 171 100 151
 <ENTER>

//compiled 32-Bit
Speedtest for statesize of 64 bits
44
cycles per Byte : 128.56

The task
 220 197 147 174 117  97 149 171 100 151
 <ENTER>

PerlEdit

Translation of: Raku
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 = Automaton->new(30, 1, map 0, 1 .. 100);

for my $n (1 .. 10) {
    my $sum = 0;
    for my $b (1 .. 8) {
	$sum = $sum * 2 + $a->{cells}[0];
	$a->next;
    }
    print $sum, $n == 10 ? "\n" : " ";
}
Output:
220 197 147 174 117 97 149 171 240 241

PhixEdit

Making the minimum possible changes to Elementary_cellular_automaton#Phix, output matches C, D, Go, J, Kotlin, Racket, and zkl, and with the changes marked [2] C++, Haskell, Perl, Python, Ruby, Scheme, and Sidef, but completely different to Rust and Tcl. No attempt to optimise.

with javascript_semantics
--string s = ".........#.........", --(original)
string s = "...............................#"&
           "................................", 
--string s = "#"&repeat('.',100),   -- [2]
       t=s, r = "........"
integer rule = 30, k, l = length(s), w = 0
for i=1 to 8 do
    r[i] = iff(mod(rule,2)?'#':'.')
    rule = floor(rule/2)
end for
sequence res = {}
for i=0 to 80 do
    w = w*2 + (s[32]='#')
--  w = w*2 + (s[1]='#')            -- [2]
    if mod(i+1,8)=0 then res&=w w=0 end if
    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
pp(res)
Output:
{220,197,147,174,117,97,149,171,100,151}
Output:

with the changes marked [2]

{220,197,147,174,117,97,149,171,240,241}

PythonEdit

Python: With zero padded endsEdit

from elementary_cellular_automaton import eca, eca_wrap

def rule30bytes(lencells=100):
    cells = '1' + '0' * (lencells - 1)
    gen = eca(cells, 30)
    while True:
        yield int(''.join(next(gen)[0] for i in range(8)), 2)

if __name__ == '__main__':
    print([b for i,b in zip(range(10), rule30bytes())])
Output:
[255, 255, 255, 255, 255, 255, 255, 255, 255, 255]

!

Python: With wrapping of end cellsEdit

def rule30bytes(lencells=100):
    cells = '1' + '0' * (lencells - 1)
    gen = eca_wrap(cells, 30)
    while True:
        yield int(''.join(next(gen)[0] for i in range(8)), 2))
Output:
[220, 197, 147, 174, 117, 97, 149, 171, 240, 241]

RacketEdit

Implementation of Elementary cellular automaton is saved in "Elementary_cellular_automata.rkt"

#lang racket
;; below is the code from the parent task
(require "Elementary_cellular_automata.rkt")
(require racket/fixnum)

;; This is the RNG automaton
(define (CA30-random-generator
         #:rule [rule 30] ; rule 30 is random, maybe you're interested in using others
         ;; width of the CA... this is implemented as a number of words plus,
         ;; maybe, another word containing the spare bits
         #:bits [bits 256])
  (define-values [full-words more-bits]
    (quotient/remainder bits usable-bits/fixnum))
  (define wrap-rule
    (and (positive? more-bits) (wrap-rule-truncate-left-word more-bits)))
  (define next-gen (CA-next-generation 30 #:wrap-rule wrap-rule))
  (define v (make-fxvector (+ full-words (if more-bits 1 0))))
  (fxvector-set! v 0 1) ; this bit will always have significance

  (define (next-word)
    (define-values [v+ o] (next-gen v 0))
    (begin0 (fxvector-ref v 0) (set! v v+)))

  (lambda (bits)
    (for/fold ([acc 0]) ([_ (in-range bits)])
      ;; the CA is fixnum, but this function returns integers of arbitrary width
      (bitwise-ior (arithmetic-shift acc 1) (bitwise-and (next-word) 1)))))

(module+ main
  ;; To match the other examples on this page, the automaton is 30+30+4 bits long
  ;; (i.e. 64 bits)
  (define C30-rand-64 (CA30-random-generator #:bits 64))
  ;; this should be the list from "C"
  (for/list ([i 10]) (C30-rand-64 8))

  ; we also do big numbers...
  (number->string (C30-rand-64 256) 16)
  (number->string (C30-rand-64 256) 16)
  (number->string (C30-rand-64 256) 16)
  (number->string (C30-rand-64 256) 16))
Output:
(220 197 147 174 117 97 149 171 100 151)
"ecd9fbcdcc34604d833950deb58447124b98706e74ccc74d9337cb4e53f38c5e"
"9c8b6471a4bc2cb3508f10b6635e4eb959ad8bbe484480695e8ddb5795f956a"
"6d85153a987dad6f013bc6159a41bf95b9d9b14af87733e17c702a3dc9052172"
"fc6fd302f5ea8f2fba6f476cfe9d090dc877dbd558e5afba49044d05b14d258"

RakuEdit

(formerly Perl 6)

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(30), :cells( flat 1, 0 xx 100 );

say :2[$a++.cells[0] xx 8] xx 10;
Output:
220 197 147 174 117 97 149 171 240 241

RubyEdit

size = 100
eca = ElemCellAutomat.new("1"+"0"*(size-1), 30)
eca.take(80).map{|line| line[0]}.each_slice(8){|bin| p bin.join.to_i(2)}
Output:
220
197
147
174
117
97
149
171
240
241

RustEdit

//Assuming the code from the Elementary cellular automaton task is in the namespace.
fn main() {
    struct WolfGen(ElementaryCA);
    impl WolfGen {
        fn new() -> WolfGen {
            let (_, ca) = ElementaryCA::new(30);
            WolfGen(ca)
        }
        fn next(&mut self) -> u8 {
            let mut out = 0;
            for i in 0..8 {
                out |= ((1 & self.0.next())<<i)as u8;
            }
            out
        }
    }
    let mut gen = WolfGen::new();
    for _ in 0..10 {
        print!("{} ", gen.next());
    }
}
Output:
157 209 228 58 87 195 212 106 147 244 

SchemeEdit

; uses SRFI-1 library http://srfi.schemers.org/srfi-1/srfi-1.html

(define (random-r30 n)
  (let ((r30 (vector 0 1 1 1 1 0 0 0)))
    (fold
      (lambda (x y ls)
	(if (= x 1)
	  (cons (* x y) ls)
	  (cons (+ (car ls) (* x y)) (cdr ls))))
      '()
      (circular-list 1 2 4 8 16 32 64 128)
      (unfold-right
	(lambda (x) (zero? (car x)))
	cadr
	(lambda (x) (cons (- (car x) 1)
			  (evolve (cdr x) r30)))
	(cons (* 8 n) (cons 1 (make-list 79 0))))))) ; list

(random-r30 10)
Output:
(220 197 147 174 117 97 149 171 240 241)

SidefEdit

var auto = Automaton(30, [1] + 100.of(0));

10.times {
    var sum = 0;
    8.times {
        sum = (2*sum + auto.cells[0]);
        auto.next;
    };
    say sum;
};
Output:
220
197
147
174
117
97
149
171
240
241

TclEdit

Works with: Tcl version 8.6
oo::class create RandomGenerator {
    superclass ElementaryAutomaton
    variable s
    constructor {stateLength} {
	next 30
	set s [split 1[string repeat 0 $stateLength] ""]
    }

    method rand {} {
	set bits {}
	while {[llength $bits] < 8} {
	    lappend bits [lindex $s 0]
	    set s [my evolve $s]
	}
	return [scan [join $bits ""] %b]
    }
}

Demonstrating:

set rng [RandomGenerator new 31]
for {set r {}} {[llength $r]<10} {} {
    lappend r [$rng rand]
}
puts [join $r ,]
Output:
220,197,147,174,241,126,135,130,143,234

Note that as the number of state bits is increased (the parameter to the constructor), the sequence tends to a limit of                       and that deviations from this are due to interactions between the state modification “wavefront” as the automaton wraps round.

WrenEdit

Translation of: Go
Library: Wren-big

As Wren cannot deal accurately with 64-bit unsigned integers and bit-wise operations thereon, we need to use BigInt here.

import "/big" for BigInt

var n = 64

var pow2 = Fn.new { |x| BigInt.one << x }

var evolve = Fn.new { |state, rule|
    for (p in 0..9) {
        var b = BigInt.zero
        for (q in 7..0) {
            var st = state.copy()
            b = b | ((st & 1) << q)
            state = BigInt.zero
            for (i in 0...n) {
                var t1 = (i > 0) ? st >> (i-1) : st >> 63
                var t2 = (i == 0) ? st << 1 : (i == 1) ? st << 63 : st << (n+1-i)
                var t3 = (t1 | t2) & 7
                if ((pow2.call(t3) & rule) != BigInt.zero) state = state | pow2.call(i)
            }
        }
        System.write(" %(b)")
    }
    System.print()
}

evolve.call(BigInt.one, 30)
Output:
 220 197 147 174 117 97 149 171 100 151

zklEdit

No attempts at extra credit and not fast.

fcn rule(n){ n=n.toString(2); "00000000"[n.len() - 8,*] + n }
fcn applyRule(rule,cells){
   cells=String(cells[-1],cells,cells[0]);  // wrap edges
   (cells.len() - 2).pump(String,'wrap(n){ rule[7 - cells[n,3].toInt(2)] })
}
fcn rand30{
   var r30=rule(30), cells="0"*63 + 1; // 64 bits (8 bytes), arbitrary
   n:=0;
   do(8){
      n=n*2 + cells[-1];          // append bit 0
      cells=applyRule(r30,cells); // next state
   }
   n
}

Note that "var" in a function is "static" in C, ie function local variables, initialized once.

do(10){ rand30().print(","); }
Output:
220,197,147,174,117,97,149,171,100,151,