Pseudorandom number generator image
- Task
Write a program that creates an image from a Pseudorandom Number Generator (PRNG) algorithm's output. The image can have the following dimensions:
- 250px by 250px : If the algorithm requires the use of prime numbers, use 8-15 bit primes.
- 500px by 500px : If the algorithm requires the use of prime numbers, use 8-15 bit primes.
- 1000px by 1000px : If the algorithm requires the use of prime numbers, use 8-32 bit primes.
- 1500px by 1500px : If the algorithm requires the use of prime numbers, use 16-64 bit primes.
- Possible Output
https://www.random.org/analysis/randbitmap-rdo.png
- See also
6502 Assembly
6502js/easy6502
The "hardware" gives us a memory-mapped port at address $00FE which contains a different random number every clock cycle. We can use this to write to video memory (there are only 16 colors so the top 4 bits of the random value are ignored.)
define vramPtr $00
define vramPtrHi $01
main:
;we're guaranteed to start off with all registers zeroed.
STA vramPtr
LDA #$02
STA vramPtrHi
LDX #4
loop:
LDA $FE ;read a random byte from the port
STA (vramPtr),y
INY
BNE loop
INC vramPtrHi
DEX
bne loop
brk ;end program
Output can be seen by copying/pasting the above code here.
Ada
-- Generate a (pseudo)random image
-- J. Carter 2023 Apr
-- Uses Ada_GUI (https://github.com/jrcarter/Ada_GUI)
with Ada.Numerics.Discrete_Random;
with Ada_GUI;
procedure Random_Image is
package Color_Random is new Ada.Numerics.Discrete_Random (Result_Subtype => Ada_GUI.RGB_Value);
Gen : Color_Random.Generator;
Image : Ada_GUI.Widget_ID;
Event : Ada_GUI.Next_Result_Info;
use type Ada_GUI.Event_Kind_ID;
begin -- Random_Image
Color_Random.Reset (Gen => Gen);
Ada_GUI.Set_Up (Title => "Random Image");
Image := Ada_GUI.New_Graphic_Area (Width => 250, Height => 250);
All_X : for X in 0 .. 249 loop
All_Y : for Y in 0 .. 249 loop
Image.Set_Pixel (X => X, Y => Y, Color => (Red => Color_Random.Random (Gen),
Green => Color_Random.Random (Gen),
Blue => Color_Random.Random (Gen),
Alpha => 1.0) );
end loop All_Y;
end loop All_X;
Wait : loop
Event := Ada_GUI.Next_Event;
exit Wait when not Event.Timed_Out and then Event.Event.Kind = Ada_GUI.Window_Closed;
end loop Wait;
Ada_GUI.End_GUI;
end Random_Image;
- Output:
Delphi
program Pseudorandom_number_generator_image;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
vcl.Graphics,
Vcl.Imaging.PngImage;
type
TRGBTriple = packed record
b: Byte;
g: Byte;
r: Byte;
end;
PRGBTripleArray = ^TRGBTripleArray;
TRGBTripleArray = array[0..999] of TRGBTriple;
function Noise(cWidth, cHeight: Integer; Color: boolean = True): TBitmap;
const
Seed = 2147483647;
var
Pixels: PRGBTripleArray;
begin
RandSeed := Seed;
Result := TBitmap.Create;
with Result do
begin
SetSize(cWidth, cHeight);
PixelFormat := pf24bit;
for var row := 0 to cHeight - 1 do
begin
Pixels := ScanLine[row];
for var col := 0 to cWidth - 1 do
begin
if Color then
begin
Pixels[col].r := random(255);
Pixels[col].g := random(255);
Pixels[col].b := random(255);
end
else
begin
var Gray := Round((0.299 * random(255)) + (0.587 * random(255)) + (0.114
* random(255)));
Pixels[col].r := Gray;
Pixels[col].g := Gray;
Pixels[col].b := Gray;
end;
end;
end;
end;
end;
const
cWidth = 1000;
cHeight = 1000;
begin
// Color noise
var bmp := Noise(cWidth, cHeight);
bmp.SaveToFile('randbitmap-rdo.bmp');
// to Png
with TPngImage.create do
begin
Assign(bmp);
SaveToFile('randbitmap-rdo.png');
free;
end;
bmp.Free;
// Gray noise
bmp := Noise(cWidth, cHeight, False);
bmp.SaveToFile('randbitmap-rdo_g.bmp');
// to Png
with TPngImage.create do
begin
Assign(bmp);
SaveToFile('randbitmap-rdo_g.png');
free;
end;
bmp.Free;
end.
- Output:
Factor
Factor's default PRNG is Mersenne Twister, but it can be easily swapped out for others like Drand, Xoroshiro, Blum Blum Shub, lagged Fibonnaci, system RNGs, and more.
USING: accessors images.testing images.viewer literals math
random sequences ;
CONSTANT: size 500
<rgb-image>
${ size size } >>dim
size sq 3 * [ 256 random ] B{ } replicate-as >>bitmap
image-window
Forth
Uses gforth random generator to create PBM portable pixmap image file.
require random.fs
: prngimage
outfile-id >r
s" prngimage.pbm" w/o create-file throw to outfile-id
s\" P1\n500 500\n" type
500 0 do
500 0 do
2 random 48 + emit
loop #lf emit
loop
outfile-id close-file throw
r> to outfile-id ;
prngimage
FreeBASIC
Windowtitle "Pseudorandom number generator image"
Dim As Integer w = 500, h = w, x, y
Screenres w, h, 16
For x = 0 To w-1
For y = 0 To h-1
Pset(x, y), Rgb(Rnd * 255, Rnd * 255, Rnd * 255)
Next y
Next x
Bsave "Pseudo-Random-Algorithm.bmp",0
image500.png (sample image, offsite)
Go
The math/rand package uses a custom algorithm attributed to D.P.Mitchell and J.A.Reeds. It doesn't need to be seeded by a prime number. Typically (as here) the seed is generated from the current time.
The image is saved to a .png file which can then be viewed with a utility such as EOG.
package main
import (
"image"
"image/color"
"image/png"
"log"
"math/rand"
"os"
"time"
)
func main() {
rand.Seed(time.Now().UnixNano())
img := image.NewNRGBA(image.Rect(0, 0, 1000, 1000))
for x := 0; x < 1000; x++ {
for y := 0; y < 1000; y++ {
col := color.RGBA{uint8(rand.Intn(256)), uint8(rand.Intn(256)), uint8(rand.Intn(256)), 255}
img.Set(x, y, col)
}
}
fileName := "pseudorandom_number_generator.png"
imgFile, err := os.Create(fileName)
if err != nil {
log.Fatal(err)
}
defer imgFile.Close()
if err := png.Encode(imgFile, img); err != nil {
imgFile.Close()
log.Fatal(err)
}
}
Java
Following implementation generates images from java.util.Random(uses linear congruential generator [4].) and Blum Blum Shub Algorithm with least significant bit method and even bit parity method[5].
import javax.imageio.ImageIO;
import java.awt.*;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.math.BigInteger;
import java.security.SecureRandom;
import java.util.Random;
import java.util.Scanner;
/*
* Numbers to try:
* p = 11 or BigInteger.probablePrime(BIT1_LENGTH, rand)
* q = 23 or BigInteger.probablePrime(BIT_LENGTH, rand)
* seed = 3 or BigInteger.probablePrime(BIT_LENGTH,rand)
* */
public class csprngBBS {
public static Scanner input = new Scanner(System.in);
private static final String fileformat = "png";
private static String bitsStri = "";
private static String parityEven = "";
private static String leastSig = "";
private static String randomJavaUtil = "";
private static int width = 0;
private static int BIT_LENGTH = 0;
private static final Random rand = new SecureRandom();
private static BigInteger p = null; // 11
private static BigInteger q = null; // 23
private static BigInteger m = null;
private static BigInteger seed = null; // 3
private static BigInteger seedFinal = null;
private static final Random randMathUtil = new SecureRandom();
public static void main(String[] args) throws IOException {
System.out.print("Width: ");
width = input.nextInt();
System.out.print("Bit-Length: ");
BIT_LENGTH = input.nextInt();
System.out.print("Generator format: ");
String useGenerator = input.next();
p = BigInteger.probablePrime(BIT_LENGTH, rand);
q = BigInteger.probablePrime(BIT_LENGTH, rand);
m = p.multiply(q);
seed = BigInteger.probablePrime(BIT_LENGTH,rand);
seedFinal = seed.add(BigInteger.ZERO);
if(useGenerator.contains("parity") && useGenerator.contains("significant")) {
findLeastSignificant();
findBitParityEven();
createImage(parityEven, "parityEven");
createImage(leastSig, "significant");
}
if(useGenerator.contains("parity") && !useGenerator.contains("significant")){
findBitParityEven();
}
if(useGenerator.contains("significant") && !useGenerator.contains("parity")){
findLeastSignificant();
createImage(leastSig, "significant");
}
if(useGenerator.contains("util")){
findRandomJava(randMathUtil);
createImage(randomJavaUtil, "randomUtilJava");
}
}
public static void findRandomJava(Random random){
for(int x = 1; x <= Math.pow(width, 2); x++){
randomJavaUtil += random.nextInt(2);
}
}
public static void findBitParityEven(){
for(int x = 1; x <= Math.pow(width, 2); x++) {
seed = seed.pow(2).mod(m);
bitsStri = convertBinary(seed);
char[] bits = bitsStri.toCharArray();
int counter = 0;
for (char bit : bits) {
if (bit == '1') {
counter++;
}
}
if (counter % 2 != 0) {
parityEven += "1";
} else {
parityEven += "0";
}
}
}
public static void findLeastSignificant(){
seed = seedFinal;
for(int x = 1; x <= Math.pow(width, 2); x++){
seed = seed.pow(2).mod(m);
leastSig += bitsStri.substring(bitsStri.length() - 1);
}
}
public static String convertBinary(BigInteger value){
StringBuilder total = new StringBuilder();
BigInteger two = BigInteger.TWO;
while(value.compareTo(BigInteger.ZERO) > 0){
total.append(value.mod(two));
value = value.divide(two);
}
return total.reverse().toString();
}
public static void createImage(String useThis, String fileName) throws IOException {
int length = csprngBBS.width;
// Constructs a BufferedImage of one of the predefined image types.
BufferedImage bufferedImage = new BufferedImage(length, length, 1/*BufferedImage.TYPE_INT_RGB*/);
// Create a graphics which can be used to draw into the buffered image
Graphics2D g2d = bufferedImage.createGraphics();
for (int y = 1; y <= length; y++) {
for (int x = 1; x <= length; x++) {
if (useThis.startsWith("1")) {
useThis = useThis.substring(1);
g2d.setColor(Color.BLACK);
g2d.fillRect(x, y, 1, 1);
} else if (useThis.startsWith("0")) {
useThis = useThis.substring(1);
g2d.setColor(Color.WHITE);
g2d.fillRect(x, y, 1, 1);
}
}
System.out.print(y + "\t");
}
// Disposes of this graphics context and releases any system resources that it is using.
g2d.dispose();
// Save as file
File file = new File("REPLACEFILEPATHHERE" + fileName + "." + fileformat);
ImageIO.write(bufferedImage, fileformat, file);
}
}
jq
Works with jq and gojq, the C and Go implementations of jq
It has been claimed that the elementary cellular automaton with "Rule 30" can be used as a PRNG, (see e.g. Elementary_cellular_automaton/Random_number_generator), so this entry generates a set of (x,y,color) co-ordinates so that this hypothesis might be visually evaluated e.g. using the gnuplot program.
To keep things brief, the jq filter definitions at Elementary_cellular_automaton#jq are used but not repeated here.
include "elementary-cellular-automaton" {search : "."}; # the defs at [[Elementary_cellular_automaton#jq]]
def binary2number:
reduce (.[]|tonumber) as $x ({p:1}; .n += .p * $x | .p *= 2) | .n;
# Emit a stream of $n PRNGs in range(0;255)
def prng($n):
# 30 is 11110
("1" + 100 * "0" )
| [automaton(30; 8 * $n) | .[0:1]]
| _nwise(8) | binary2number ;
foreach prng(99*99) as $color ({x:0, y:1};
.color = $color
| .x += 1
| if .x == 100 then .x = 1 | .y += 1 else . end )
| "\(.x) \(.y) \(.color)"
Invocation:
jq -nrf program.jq > prng.txt gnuplot plot("prng.txt") with image pixels
Julia
Julia uses the Mersenne Twister algorithm for its default rand() function. That algorithm uses over 600 32-bit ints to represent its internal state, rather than just a product of two or three primes.
using FileIO, ImageIO
save("randombw.png", rand(Float16, 1000, 1000))
Lua
Lua uses the xoroshiro256**
algorithm.
size = 500
math.randomseed(os.time())
-- Writes a 256-bit grayscale PGM image file:
function writePgm(data, fn, comment)
local rows = #data
local cols = #data[1]
local file = io.open(fn, "wb")
-- Write header in ASCII
file:write("P5", "\n")
if comment ~= nil then
file:write("# ", comment, "\n")
end
file:write(cols, " ", rows, "\n")
file:write("255", "\n")
-- Write data in raw bytes
for _, r in ipairs(data) do
file:write(string.char(unpack(r)))
end
file:close()
end
img = {}
for r = 1, size do
img[r] = {}
for c = 1, size do
img[r][c] = math.random(0,255)
end
end
writePgm(img, "prng_img.pgm", string.format("PRNG Image (%d x %d)", size, size))
Maxima
genmatrix(lambda([i,j],random(1000)),1000,1000)$
wxdraw2d(image(%,0,0,30,30));
Nim
Nim standard PRNG is an implementation of the xoroshiro128+
(xor/rotate/shift/rotate) algorithm which is extremely fast. The standard library provides a Mersenne Twister implementation too. For this task, we used the first one.
import random
import imageman
const Size = 500
randomize()
var image = initImage[ColorRGBU](Size, Size)
for x in 0..<Size:
for y in 0..<Size:
let color = ColorRGBU([rand(255).byte, rand(255).byte, rand(255).byte])
image[x, y] = color
image.savePNG("prng_image.png", compression = 9)
Perl
Perl unified the PRNG with its own internal drand48() implementation on all platforms since v5.20.0. Without a manual srand, Perl by default source the seed from "/dev/urandom" if it is available so there shouldn't be any prime prerequisite.
use strict;
use warnings;
use GD;
my $img = GD::Image->new(500, 500, 1);
for my $y (0..500) {
for my $x (0..500) {
my $color = $img->colorAllocate(rand 256, rand 256, rand 256);
$img->setPixel($x, $y, $color);
}
}
# using "use v5.38.0;" enables strict and warnings automatically and results with the following error (twice):
# These fail with strict and warnings enabled (Bareword filehandle "F" not allowed under 'no feature "bareword_filehandles"')
# open F, "image500.png";
# print F $img->png;
# Replace with (although the close is not required, it is a good habit):
open (my $fh, ">", "image500.png") or die "Can't open image500.png: $!";
print $fh $img->png;
close ($fh) or warn "Unable to close file handle associated with image500.png after writing: $!";
image500.png (sample image, offsite)
Phix
-- demo\rosetta\Pseudorandom_number_generator_image.exw without js -- IupSaveImage(), not possible from within a browser (though a "save" button might be?) include pGUI.e IupOpen() integer w=250, h=w sequence bw = repeat(0,w*h) for x=0 to w-1 do for y=0 to h-1 do if rand(2)=2 then bw[x*h+y+1] = 255 end if end for end for Ihandle image = IupImage(w,h,bw) object res = IupSaveImage(image,"bw.png","PNG") IupClose()
PicoLisp
(seed (in "/dev/urandom" (rd 8)))
(out "image.pbm"
(prinl "P1")
(prinl 500 " " 500)
(do 500
(do 500
(prin (if (rand T) 1 0)) )
(prinl) ) )
Python
# pseudorandom number image generator by Xing216
from random import randbytes
from PIL import Image
size = 1500
x = bytes.fromhex(" ".join([randbytes(3).hex() for x in range(size*size)]))
img = Image.frombuffer('RGB', (size, size), x, 'raw', 'RGB', 0, 1)
img.show()
Output: rcXing216.png (transfer.sh)
Raku
MoarVM uses Mersenne Twister as its PRNG but a prime seeder is not mandatory.
# 20200818 Raku programming solution
use Image::PNG::Portable;
srand 2⁶³ - 25; # greatest prime smaller than 2⁶³ and the max my system can take
my @data = < 250 500 1000 1500 >;
@data.map: {
my $o = Image::PNG::Portable.new: :width($_), :height($_);
for ^$_ X ^$_ -> @pixel { # about 40% slower if split to ($x,$y) or (\x,\y)
$o.set: @pixel[0], @pixel[1], 256.rand.Int, 256.rand.Int, 256.rand.Int
}
$o.write: "image$_.png" or die;
}
- Output:
file image*.png image1000.png: PNG image data, 1000 x 1000, 8-bit/color RGBA, non-interlaced image1500.png: PNG image data, 1500 x 1500, 8-bit/color RGBA, non-interlaced image250.png: PNG image data, 250 x 250, 8-bit/color RGBA, non-interlaced image500.png: PNG image data, 500 x 500, 8-bit/color RGBA, non-interlaced
image500.png (sample image, offsite)
Sidef
require('GD')
var img = %O<GD::Image>.new(500, 500, 1)
for y in (0..500), x in (0..500) {
var color = img.colorAllocate(255.irand, 255.irand, 255.irand)
img.setPixel(x, y, color)
}
File("image500.png").write(img.png, :raw)
Standard ML
There is no built-in random number generator in Standard ML so we use our own implementation of SplitMix64.
structure SplitMix64 =
struct
structure W64 = Word64
val randmax = (0wxFFFFFFFFFFFFFFFF : W64.word)
(* if NONE is passed, seed using the current time *)
fun init NONE =
W64.fromLargeInt (Time.toNanoseconds (Time.now ()))
| init (SOME x) = x
fun next instate =
let
val newstate = instate + 0wx9e3779b97f4a7c15
val z1 = W64.xorb (newstate, W64.>> (newstate, 0w30))
val z2 = z1 * 0wxbf58476d1ce4e5b9
val z3 = W64.xorb (z2, W64.>> (z2, 0w27))
val z4 = z3 * 0wx94d049bb133111eb
in
(newstate, W64.xorb (z4, W64.>> (z4, 0w31)))
end
fun nextRange instate (min, max) =
let
val minword = W64.fromInt min
val maxword = W64.fromInt max
val maxfromzero = maxword - minword
val ignored_range = randmax - randmax mod maxword
val (newstate, res) = next instate
in
if res >= ignored_range then nextRange newstate (min, max)
else (newstate, (res mod maxword) + minword)
end
end
fun getRandBytes n =
let
val prng = ref (SplitMix64.init NONE)
fun nextRand _ =
let val (prng', res) = SplitMix64.nextRange (!prng) (0, 255)
in prng := prng'; Word8.fromInt (Word64.toInt res)
end
in
Word8Vector.tabulate (n, nextRand)
end
fun binPrint ostrm s =
BinIO.output (ostrm, Byte.stringToBytes s)
fun printPPMHeader ostrm (width, height) =
let
val bprint = binPrint ostrm
in
( bprint "P6\n"
; bprint (Int.toString width)
; bprint " "
; bprint (Int.toString height)
; bprint "\n255\n"
)
end
fun printRandomPPM ostrm (width, height) =
let
(* multiply by three for R G B *)
val bytes = getRandBytes width * height * 3
in
(printPPMHeader ostrm (width, height); BinIO.output (ostrm, bytes))
end
fun showUsage () =
( print "Usage: "
; print (CommandLine.name ())
; print " <output_name> [width] [height]\n"
; print " width and height default to 512 if not specified\n"
; OS.Process.exit OS.Process.failure
)
fun parseArgs [] = showUsage ()
| parseArgs [outname] = {outname = outname, width = 512, height = 512}
| parseArgs [outname, width, height] =
{ outname = outname
, width = valOf (Int.fromString width)
, height = valOf (Int.fromString height)
}
| parseArgs _ = showUsage ()
fun main () =
let
val {outname, width, height} = parseArgs (CommandLine.arguments ())
val ostrm = BinIO.openOut outname
in
printRandomPPM ostrm (width, height) before BinIO.closeOut ostrm
end
val () = main ()
Wren
DOME's 'random' module uses a pseudorandom number generator based on the Squirrel3 (optionally Squirrel5) noise function which doesn't need to be seeded with a prime number. Typically (as here) the seed is generated from the current system time.
import "dome" for Window
import "graphics" for Canvas, Color
import "random" for Random
class Game {
static init() {
Window.title = "Pseudorandom Number Generator Image"
Window.resize(1000, 1000)
Canvas.resize(1000, 1000)
var r = Random.new() // generates seed from current time
for (x in 0...1000) {
for (y in 0...1000) {
var c = Color.rgb(r.int(256), r.int(256), r.int(256))
Canvas.pset(x, y, c)
}
}
}
static update() {}
static draw(dt) {}
}
XPL0
The PRNG is linear congruential and is built-in. It's seeded with the time-of-day.
int X, Y;
[SetVid($11B); \VESA 1280x1024x24
for Y:= 0 to 1000-1 do
for X:= 0 to 1000-1 do
Point(X, Y, Ran($100_0000));
]
- Output:
Essentially the same as Delphi's image.