AWK, 266 bytes

func r(G){return int(rand()*G)}func c(){return"\033[48;5;"r(256)"m \033[0m"}BEGIN{for(srand();i++<40;)for(j=0;j++<80;)a[j][i]=c()
for(;k++<1e4;){system("sleep 0.2");a[r(80)+1][r(40)+1]=c();for(x=40;x--;print)for(y=80;y--;)printf a[y][x];for(t=40;t--;)print"\033[A"}}

I recommend you do not run this. AWK doesn't have fancy screen manipulation, so this is flashy monstrosity. It's giving me a headache. Might be risky if you have epilepsy even.

MATL, 28 bytes

40tI3$l`3l2$r,40Yr]4$Y(t3YGT

Try it at MATL Online. I have added a half-second pause (.5Y.) to this version.

Explanation

40       % Push the number literal 40 to the stack
t        % Duplicate
I        % Push the number 3 to the stack
3$l      % Create a 40 x 40 x 3 matrix of 1's (40 x 40 RGB image)
`        % Do...while loop
  3l1$r  % Generate 3 random numbers (RGB)
  ,      % Do twice loop
    40Yr % Generate two integers between 1 and 40. These will be the
  ]      % row and column of the pixel to replace
  4$Y(   % Replace the pixel with the random RGB value
  t      % Make a copy of the RGB image
  3YG    % Display the image
  T      % Push a literal TRUE to create an infinite loop

PostScript, 151 bytes

realtime srand[/PageSize[640 640]>>setpagedevice
10 10 scale([){rand 16#7fffffff div}def(]){rand 64 mod}def{[[[setrgbcolor]]1 1 rectfill flushpage}loop

Needs ghostscript for flushpage; not very fast! Maybe 100 pixels/second on my machine.

TI-Basic (83/84(+(SE)) only), 33 bytes

For(I,0,62
For(J,0,94
If int(2rand
Pxl-Change(I,J
End
End
prgmC

^{where C is the name of the program.}

Without calling itself (+2 bytes):

While 1
For(I,0,62
For(J,0,94
If int(2rand
Pxl-Change(I,J
End
End
End

The TI-83 family calculators with monochrome screens (TI-83, TI-83+, TI-83+SE, TI-84+, and TI-84+SE) support only black and white as colors. This program goes through all the pixels on the screen (except for the rightmost column and bottommost row) and has a 50% chance of inverting it. This may take more than 3 minutes depending on the calculator; if so, replacing 62 and 94 with 39 each should work.

Java, 401 383 373 bytes

Golfed version:

import java.awt.image.*;import java.util.*;class R{public static void main(String[]a){new javax.swing.JFrame(){int w=200;BufferedImage i=new BufferedImage(w,w,1);Random r=new Random();{setSize(w,w);show();new Thread(()->{for(;;){i.setRGB(r.nextInt(w),r.nextInt(w),r.nextInt(1<<24));repaint();}}).start();}public void paint(java.awt.Graphics g){g.drawImage(i,0,0,null);}};}}

Ungolfed version:

import java.awt.image.*;
import java.util.*;

class R {
    public static void main(String[] a) {
        new javax.swing.JFrame() {
            int w = 200;                           // a constant for width and height
            BufferedImage i = new BufferedImage(
                                        w, w,      // image width and height
                                        1);        // image type BufferedImage.TYPE_INT_RGB
            Random r = new Random();
            {
                setSize(w, w);                     // frame big enough for image
                show();                            // make the frame visible
                new Thread(() -> {                 // create a forever running thread
                    for(;;) {
                        i.setRGB(
                             r.nextInt(w),         // random x position in range 0 .. w-1
                             r.nextInt(w),         // random y position in range 0 .. w-1
                             r.nextInt(1 << 24));  // random RGB value in range 0x000000 .. 0xFFFFFF
                        repaint();                 // trigger a call to the paint method
                    }
                }).start();                        // start the thread
            }

            public void paint(java.awt.Graphics g) {
                g.drawImage(i, 0, 0, null);        // draw the whole image at x=0, y=0
            }
        };
    }
}

Result:

Powershell, 128 126 124 88 bytes

-2 bytes thanks @Veskah

1..($c=[Console])::WindowWidth*$c::WindowHeight|%{Write-Host ' '-b(random 16)-n}
for(){}

Output:

VS code output:

Batch 165 156 bytes

• \E must be replaced with escape character OR download original from pastebin
• requires windows 10 with virtual terminal sequences enabled
• note: code contains trailing whitespace

@mode 40,40&@Setlocal EnableDelayedExpansion&@For /l %%i in ()Do @Set/AY=!random!%%40+1,X=!random!%%40+1,c=!random!%%256+1&<nul Set/p=\E[!Y!;!X!H\E[48;5;!c!m 

Racket (ISL w/ lambda + universe.rkt), 168 bytes

(define(r x)(random x))(big-bang(empty-scene 40 40)[to-draw(lambda(x)x)][on-tick(lambda(x)(place-image(square 1'solid(make-color(r 255)(r 255)(r 255)))(r 40)(r 40)x))])

Ungolfed:

(define (r x) (random x))
(big-bang (empty-scene 40 40)
  [to-draw (lambda (x) x)]
  [on-tick (lambda (x) (place-image (square 1 "solid" (make-color (r 255) (r 255) (r 255))) (r 40) (r 40) x))])

Pretty simple, just places a randomly-colored 1-pixel square at a random location from 0 to 40.

Output after ~3 minutes:

_{Can anyone guess what book I've been reading, given my language choice?}

Commodore 64 (old ROM I think), ~28 tokenized BASIC Bytes used

 0poke646,rnd(.)*16:?"{reverse on} ";:goto

The memory location 646 is used as a colour out in the BASIC kernal (pretty sure this is the old kernal, not the C64c kernal), which is one of the 16 colours available in its palette. Then a reverse space is printed after. goto is used as an infinite loop until the screen is filled.

This is the cheapest in terms of bytes. There is a nicer way to do this, as follows:

Commodore 64 (new and old ROM), ~46 tokenized BASIC bytes

 0 fori=0to999:poke1024+i,160:poke55296+i,rnd(.)*16:next

This will poke firstly a reversed (or inversed) space to the screen RAM (at 0x0400 - 0x07e7), and then alter the colour attribute for each character position (mapped at 0xd800 - 0xdbe7) between 0 and 15 inclusive.

As soon as the for/next loop ends, the ready. prompt is shown. To stop this, add the following line, costing another 7 tokenized BASIC bytes:

 1 go to 1

SmileBASIC, 43 41 40 bytes

GPSET RND(40),RND(40),-1-RND(1<<24)EXEC.

I use -1-RND(1<<24) to generate the random color. RND(1<<24) generates a number from 0x000000 to 0xFFFFFF, and -1 - n (equivalent to bitwise NOT) will set the alpha to 0xFF (and flip the bits of the color data but that won't affect the randomness).

PHP, 194 bytes

My previous answer did not animate; this one does.

<?session_register("i");$i||imagecreatetruecolor(64,64);imagesetpixel($i,rand(64)%,rand()%64,rand()%2**24);header("Content-Type: image/png");header("Location: ".basename(__FILE__));imagepng($i);

save to file, call in browser. It´s as fast as your browser can refresh.
Probably not able to set 4096 pixels in 180 seconds though.

breakdown

<?                                                  # start PHP
session_register("i");                              # register image in session
$i||imagecreatetruecolor(64,64);                    # if no image exists, create one
imagesetpixel($i,rand(64)%,rand()%64,rand()%2**24); # set a random pixel to random color
header("Content-Type: image/png");                  # send HTTP header for image 
header("Location: ".basename(__FILE__));            # send HTTP header to reload
imagepng($i);                                       # send image data

Minecraft 1.12.2, 747 bytes(compressed), 836+60(contain+filename)

0000h: 52 61 72 21 1A 07 01 00 F3 E1 82 EB 0B 01 05 07
0010h: 00 06 01 01 80 80 80 00 8A 2C 8F 18 25 02 03 0B
0020h: 94 01 04 94 01 20 D2 9C B3 95 80 00 00 09 6C 65
0030h: 76 65 6C 2E 64 61 74 0A 03 02 F0 E3 51 1A 04 6E
0040h: D4 01 1F 8B 08 00 34 EB D4 5B 00 FF E3 62 60 E0
0050h: 62 60 71 49 2C 49 E4 60 E0 4D 4F CD 4B 2D 4A 2C
0060h: C9 2F F2 4B CC 4D 65 60 49 CB 49 2C 61 66 E0 70
0070h: 07 72 42 2A 0B 52 19 18 18 98 99 19 D8 CB 52 8B
0080h: 8A 33 F3 F3 18 18 BC F6 72 31 70 82 24 83 4A 73
0090h: 52 8B 39 18 04 D2 81 6C 9F FC FC 02 B7 D2 BC E4
00a0h: 12 90 12 C6 44 06 66 06 B6 E0 82 C4 F2 BC 28 06
00b0h: 90 76 28 27 02 C4 01 69 80 D9 E7 5F 00 52 5F CC
00c0h: C0 69 6C 6D 64 6A A6 65 68 6D C8 C0 00 00 20 45
00d0h: 88 30 9A 00 00 00 C6 A9 60 BA 41 02 03 0B 92 01
00e0h: 04 A9 02 20 58 56 55 04 80 03 00 25 64 61 74 61
00f0h: 2F 66 75 6E 63 74 69 6F 6E 73 2F 6D 69 6E 65 63
0100h: 72 61 66 74 2F 61 2E 6D 63 66 75 6E 63 74 69 6F
0110h: 6E 0A 03 02 76 DA 2D 12 05 6E D4 01 C6 13 8F 20
0120h: 54 43 33 F6 50 34 BD 83 E0 EA 70 08 12 22 42 4A
0130h: 60 4E 1F 06 31 44 F5 04 06 DA 42 5A 88 DD 2F BB
0140h: BD 07 AD 36 E9 75 3E 23 86 E9 A6 7C 51 B9 C9 72
0150h: 8C 30 CF 07 83 D9 46 51 EB 3D C3 E1 1B 2C 6D A8
0160h: 53 C1 54 83 18 0B 1A 57 5B 63 54 F3 41 D9 97 53
0170h: AB 55 E0 F8 23 A6 81 32 D7 B0 F8 37 B8 3D 72 D5
0180h: 3A 27 98 2E 39 A2 20 68 BC BA DB FE 84 61 A0 17
0190h: 19 D0 97 3C FA 9E 71 98 92 87 6C 7C 93 DF E5 D9
01a0h: AC 8D AB 1F C7 4C FB 91 29 D4 59 3E 3B 90 1B C0
01b0h: AA 3A 41 02 03 0B E8 00 04 87 03 20 19 8F C5 65
01c0h: 80 03 00 25 64 61 74 61 2F 66 75 6E 63 74 69 6F
01d0h: 6E 73 2F 6D 69 6E 65 63 72 61 66 74 2F 62 2E 6D
01e0h: 63 66 75 6E 63 74 69 6F 6E 0A 03 02 22 1C 99 C6
01f0h: 02 6E D4 01 C6 F9 65 26 43 54 2F 76 04 3E E8 34
0200h: 3E D0 28 3E DF E5 3A A3 C9 D0 DE 0A 0F 3D BE 27
0210h: 9F C7 2F 2E B4 CC E1 30 81 32 A5 81 33 0C A0 F2
0220h: 43 EA 5B 6D 37 CA 74 CF 55 55 55 C0 BC 9E 29 49
0230h: A8 9D 7D DF 02 97 B4 1E B6 60 16 80 58 18 31 01
0240h: A3 62 07 0A 46 3C 51 E4 80 A0 08 89 E0 90 AD 7F
0250h: DF 2E AF CE 23 A6 91 E3 48 FA D0 1C BA A1 75 20
0260h: 32 02 03 0B 00 05 00 10 00 00 00 00 80 00 00 18
0270h: 64 61 74 61 2F 66 75 6E 63 74 69 6F 6E 73 2F 6D
0280h: 69 6E 65 63 72 61 66 74 0A 03 02 AD C3 9B 2D 04
0290h: 6E D4 01 C4 B1 B7 E8 28 02 03 0B 00 05 00 10 00
02a0h: 00 00 00 80 00 00 0E 64 61 74 61 2F 66 75 6E 63
02b0h: 74 69 6F 6E 73 0A 03 02 D1 6A 8E 26 25 6D D4 01
02c0h: F6 87 4C DB 1E 02 03 0B 00 05 00 10 00 00 00 00
02d0h: 80 00 00 04 64 61 74 61 0A 03 02 EE 28 D1 1F 25
02e0h: 6D D4 01 1D 77 56 51 03 05 04 00               

To prove whole world is not always bigger (bin is .rar file)

level.dat
    Data
        GameRules
            gameLoopFunction: a
        GameType: 3 # so you don't fall and mob won't spawn at night
        generatorName: flat
        generatorOptions: 3;256*1;1 # full of stone
        SpawnX: 0
        SpawnZ: 0
        version: 19133 # avaliable
data
    functions
        minecraft
            a.mcfunction
                summon area_effect_cloud
                # won't show something when die
                spreadplayers 0 0 0 20 0 @e[type=!player]
                execute @r[type=!cow] ~ ~ ~ tp @s ~ ~-1 ~
                execute @r[type=!cow] ~ ~ ~ tp @s ~ ~-2 ~
                execute @r[type=!cow] ~ ~ ~ tp @s ~ ~-4 ~
                execute @r[type=!cow] ~ ~ ~ tp @s ~ ~-8 ~
                # minecraft bug, tp @r[type=!cow] ~ ~-1 ~
                # always tp player
                execute @e[type=!player] ~ ~ ~ function b
                tp @a ~ 275 ~
            b.mcfunction
                setblock ~ ~-1 ~ wool 15
                setblock ~ ~ ~ wool 14
                setblock ~ ~1 ~ wool 13
                setblock ~ ~2 ~ wool 12
                setblock ~ ~3 ~ wool 11
                setblock ~ ~4 ~ wool 10
                setblock ~ ~5 ~ wool 9
                setblock ~ ~6 ~ wool 8
                setblock ~ ~7 ~ wool 7
                setblock ~ ~8 ~ wool 6
                setblock ~ ~9 ~ wool 5
                setblock ~ ~10 ~ wool 4
                setblock ~ ~11 ~ wool 3
                setblock ~ ~12 ~ wool 2
                setblock ~ ~13 ~ wool 1
                setblock ~ ~14 ~ wool

Minecraft 1.12.2, 806 bytes(compressed), 1352+60(contain+filename)

0000h: 52 61 72 21 1A 07 01 00 F3 E1 82 EB 0B 01 05 07
0010h: 00 06 01 01 80 80 80 00 33 72 E7 9F 41 02 03 0B
0020h: 9E 01 04 EF 02 20 EC 92 16 D1 80 03 00 25 64 61
0030h: 74 61 2F 66 75 6E 63 74 69 6F 6E 73 2F 6D 69 6E
0040h: 65 63 72 61 66 74 2F 61 2E 6D 63 66 75 6E 63 74
0050h: 69 6F 6E 0A 03 02 E4 73 98 96 26 6D D4 01 C3 02
0060h: 9B 26 54 34 33 F6 60 34 BD 83 E0 EA 70 08 12 39
0070h: 28 94 C0 7C 3E 10 66 FE 16 83 86 B6 99 BF 88 E6
0080h: D3 3B BB 70 16 9A C8 4B E7 0E 41 82 48 CF 65 19
0090h: C9 73 C2 CC A1 21 60 7A 8F 07 DC 61 F1 C3 02 C4
00a0h: 10 E1 45 C2 C6 0A A1 72 9A 51 5D 75 32 F6 B4 37
00b0h: D9 C0 39 51 69 A4 D3 32 26 D7 53 D4 46 24 91 91
00c0h: 60 49 F1 31 DF E4 5E 70 D6 7D 20 17 39 24 6C 1F
00d0h: 47 FA 30 10 B5 DD A1 2C 87 AE E3 0C FB 87 BA 67
00e0h: E9 72 6A 24 2E D8 EB 5F F2 E3 FC 1B 66 9C F4 E9
00f0h: AA 3A FB 3C FA 7B 23 89 D4 8E E8 90 4C 1E F8 90
0100h: 41 02 03 0B 9C 01 04 CA 06 20 D0 72 7A 6E 80 03
0110h: 00 25 64 61 74 61 2F 66 75 6E 63 74 69 6F 6E 73
0120h: 2F 6D 69 6E 65 63 72 61 66 74 2F 62 2E 6D 63 66
0130h: 75 6E 63 74 69 6F 6E 0A 03 02 5E 12 89 DC 26 6D
0140h: D4 01 C7 04 99 26 54 33 33 F6 60 44 DF 42 F0 77
0150h: C1 1B 71 D9 F8 D1 42 F0 FA 52 8E BA B5 56 0E 0D
0160h: 4A 5B 74 DE F1 9A 23 93 54 07 17 13 42 46 02 5E
0170h: D4 BD C8 F3 F2 96 06 70 5F 7B EE 24 78 CC 9F E7
0180h: 18 BF F1 4C D4 BD 69 BA 63 A1 F1 E0 5F 4A 1E F2
0190h: 2A 4D 5F D4 EA 59 96 5E 23 28 7A A4 B4 AF 92 94
01a0h: 76 74 EA 70 94 CB BB F9 B3 97 64 00 AC F6 EE 0D
01b0h: C1 B8 65 81 D8 31 A1 B4 63 03 60 C5 86 B1 78 24
01c0h: 2C 2B 86 F0 AF 17 70 57 0B B4 2B 45 A4 85 AE 87
01d0h: A4 87 57 42 24 83 AE 82 49 03 B8 80 4B E6 66 BD
01e0h: 96 D5 25 02 03 0B 8F 01 04 8F 01 20 83 7C 6D FD
01f0h: 80 00 00 09 6C 65 76 65 6C 2E 64 61 74 0A 03 02
0200h: 10 70 3C 51 27 6D D4 01 1F 8B 08 00 C9 78 D3 5B
0210h: 00 FF 35 8D 41 0A C2 30 14 44 47 D2 6A 1A 28 78
0220h: 14 C5 65 B7 62 41 A4 05 75 21 EE 3E F2 5B 84 9A
0230h: 84 24 55 3C 9C 77 B3 1F 74 37 8F 79 C3 18 C0 20
0240h: DB 52 22 8D B2 67 CB 81 92 0B 0D 3D 18 59 37 50
0250h: 52 D0 F5 04 E7 B7 67 00 4A 61 F1 E4 10 EF CE 02
0260h: FB 8F 41 21 E5 71 1C 38 6A 2C FB 29 1F 9C F3 BB
0270h: D1 DE 92 28 33 82 C2 FC E4 E9 65 AF 90 F9 0F 2E
0280h: 02 32 F8 FF B5 5E FC 88 7C 53 AD AA 35 F0 05 F9
0290h: 41 3F 00 96 00 00 00 1B 7A 52 1B 32 02 03 0B 00
02a0h: 05 00 10 00 00 00 00 80 00 00 18 64 61 74 61 2F
02b0h: 66 75 6E 63 74 69 6F 6E 73 2F 6D 69 6E 65 63 72
02c0h: 61 66 74 0A 03 02 BB 8F 67 2F 25 6D D4 01 C4 B1
02d0h: B7 E8 28 02 03 0B 00 05 00 10 00 00 00 00 80 00
02e0h: 00 0E 64 61 74 61 2F 66 75 6E 63 74 69 6F 6E 73
02f0h: 0A 03 02 D1 6A 8E 26 25 6D D4 01 F6 87 4C DB 1E
0300h: 02 03 0B 00 05 00 10 00 00 00 00 80 00 00 04 64
0310h: 61 74 61 0A 03 02 EE 28 D1 1F 25 6D D4 01 1D 77
0320h: 56 51 03 05 04 00                              



level.dat
    Data
        GameRules
            gameLoopFunction: a
        GameType: 3 # so you don't fall and mob won't spawn at night
        generatorName: flat
        generatorOptions: 3;0;1 # just air
        SpawnX: 0
        SpawnZ: 0
        version: 19133 # avaliable
data
    functions
        minecraft
            a.mcfunction
                summon area_effect_cloud
                # won't show something when die
                fill -20 3 -20 20 3 20 wool
                # init. A .mca is at least 12KB too expensive
                # (though flat generation may work fine)
                scoreboard objectives add a dummy
                execute @r[type=!cow] ~ ~ ~ scoreboard players add @s a 1
                execute @r[type=!cow] ~ ~ ~ scoreboard players add @s a 2
                execute @r[type=!cow] ~ ~ ~ scoreboard players add @s a 4
                execute @r[type=!cow] ~ ~ ~ scoreboard players add @s a 8
                # minecraft bug, scoreboard players add @r[type=!cow] a 1
                # always add score to player
                execute @e[type=!player] ~ ~ ~ function b
            b.mcfunction
                spreadplayers 0 0 0 20 0 @s
                execute @s ~ 4 ~ setblock ~ ~ ~ wool
                # setblock ~ 4 ~ wool uses the old location
                execute @s[score_a=15] ~ 4 ~ setblock ~ ~ ~ wool 15
                execute @s[score_a=14] ~ 4 ~ setblock ~ ~ ~ wool 14
                execute @s[score_a=13] ~ 4 ~ setblock ~ ~ ~ wool 13
                execute @s[score_a=12] ~ 4 ~ setblock ~ ~ ~ wool 12
                execute @s[score_a=11] ~ 4 ~ setblock ~ ~ ~ wool 11
                execute @s[score_a=10] ~ 4 ~ setblock ~ ~ ~ wool 10
                execute @s[score_a=9] ~ 4 ~ setblock ~ ~ ~ wool 9
                execute @s[score_a=8] ~ 4 ~ setblock ~ ~ ~ wool 8
                execute @s[score_a=7] ~ 4 ~ setblock ~ ~ ~ wool 7
                execute @s[score_a=6] ~ 4 ~ setblock ~ ~ ~ wool 6
                execute @s[score_a=5] ~ 4 ~ setblock ~ ~ ~ wool 5
                execute @s[score_a=4] ~ 4 ~ setblock ~ ~ ~ wool 4
                execute @s[score_a=3] ~ 4 ~ setblock ~ ~ ~ wool 3
                execute @s[score_a=2] ~ 4 ~ setblock ~ ~ ~ wool 2
                execute @s[score_a=1] ~ 4 ~ setblock ~ ~ ~ wool 1

Minecraft 1.12 Redstone Command Blocks, 4,355 2,872 bytes

(Size determined by saved structure block file size.)

Here is a full YouTube overview, but I'll try to outline the code below.

Setup Routine:

This sets up the 40x40 grid of Minecraft armor stands. Armor stands are necessary because Minecraft has no way to substitute variables into world coordinates. So the workaround is to refer to the location of these armor stand entities.

(impulse) summon armor_stand 2 ~ 1 {CustomName:"A"} /create named armor stand
(chain) fill -2 ~ -2 43 ~ 43 stone                  /create big stone square
(chain) fill -1 ~ -1 42 ~ 42 air                    /leave just a ring of stone
(chain) setblock -4 ~ -12 redstone_block            /kicks off next sequence

This named armor stand is basically our "cursor" to place all the armor stands that we will need. The redstone block in the last step "powers" nearby blocks (including our command blocks), so kicks off the next loop:

(repeat) execute @e[name=A] ~ ~ ~ summon armor_stand ~-1 ~ ~   /create new armor stand 
(chain) tp @e[name=A] ~1 ~ ~                                   /move "cursor" one block
(chain) execute @e[name=A] ~ ~ ~ testforblock ~1 ~ ~ stone     /if at end of row,
(conditional) tp @e[name=A] ~-40 ~ ~1                          /go to start of next row
(chain) execute @e[name=A] ~ ~ ~ testforblock ~ ~ ~2 stone     /If at last row
(conditional) setblock ~6 ~ ~ air                              /stop looping
(conditional) kill @e[name=A]                                  /kill cursor

At this point our grid is complete:

Random Color Selector

The purple repeaters in the center of this picture choose a random color via the following command:

(repeat) execute @r[type=armor_stand,r=9] ~ ~ ~ setblock ~ ~-2 ~ redstone_block

That "@r[]" is the magic sauce, it selects a random entity in the world that matches the given conditions. In this case, it finds an armor stand inside a radius of 9 blocks, and we've set up 16 armor stands, one for each wool color. Under the selected color, it places a redstone block (which powers the two command blocks on either side).

Random Pixel Selector

Placing the redstone block under the selected wool color triggers two more command blocks:

(impulse) execute @r[type=armor_stand] ~ ~ ~ setblock ~ ~3 ~ wool X
(impulse) setblock ~ ~ ~1 air

This first line uses our same magic @r command to choose any armor stand on the entire map (no radius restriction, so that includes the 40x40 grid), and places a wool of the selected color above its head. The X determines the color, and ranges from 0 to 15. The second command removes the redstone block so it is ready to go again.

I have 5 purple repeater blocks, and redstone works in "ticks" 20 times a second, so I'm placing 100 pixels per second (minus some color overlaps). I've timed it, and I usually get the entire grid covered in about 3 minutes.

This was fun, I'll try to look for other challenges that might also work in Minecraft. Huge thanks to lorgon111 for his YouTube Command Block tutorial series.

EDIT: Made some serious reductions in the size of the saved structure, now at 2,872 saved bytes:

1. Scooted things in a bit (in all 3 dimensions) so I could reduce the overall size of the saved area.
2. Changed the different colored wools to stone, they were just decorative anyway.
3. Removed the glowstone lamp.
4. Changed all air blocks to void blocks (the red squares).

Tested by pulling the saved structure into a new world, everything still works as designed.

EDIT 2: Read-only Dropbox link to the NBT structure file

Walk through is in my YouTube video, but here are the steps:

1. In Minecraft 1.12, create a new creative superflat world using the "Redstone Ready" preset. Make it peaceful mode.
2. Once the world exists, copy the NBT file into a new \structures folder you create under the current world save.
3. Back in the game, do /give @p structure_block, and /tp @p -12, 56, -22 to jump to the right spot to get started.
4. Dig a hole and place the structure block at -12, 55, -22.
5. Right-click the structure block, click the mode button to switch it to "Load".
6. Type in "random_pixels", turn "include entities" ON, and click "Load"
7. If it finds the structure file, it will preview the outline. Right-click again and click "load" to bring the structure into the world.
8. Press the button to run the setup routine.
9. When it completes, flip the switch to run the wool randomization.

Tcl/Tk, 139

Must be run in the interactive shell

gri [can .c -w 40 -he 40]
set x 0
wh 1 {.c cr o $x [set y [exp int(rand()*40)]] $x [set x $y] -f #[form %06x [exp int(rand()*255**3)]]
upd}

Unfortunately, converting expr int(rand()* into a proc makes the script have one byte more!

To stop, one just needs to click the ineffable "X" button.

I've reused the code of present answer on https://codegolf.stackexchange.com/a/148124/29325

6502 Assembly, 582 bytes

Whew, this was fun. Does more or less the same thing as my Applesoft BASIC solution.

start:
lda #15
sta $0
sta $1
loo:
lda $fe
and #3
cmp #0
beq g_l
cmp #1
beq g_r
cmp #2
beq g_d
dec $1
d_w:
lda $1
and #$1f
asl
tax
lda ypo,x
sta $2
inx
lda ypo,x
sta $3
lda $0
and #$1f
tay
lda ($2),y
tax
inx
txa
sta ($2),y
jmp loo
g_d:
inc $1
jmp d_w
g_l:
dec $0
jmp d_w
g_r:
inc $0
jmp d_w
ypo:
dcb $00,$02,$20,$02,$40,$02,$60,$02
dcb $80,$02,$a0,$02,$c0,$02,$e0,$02
dcb $00,$03,$20,$03,$40,$03,$60,$03
dcb $80,$03,$a0,$03,$c0,$03,$e0,$03
dcb $00,$04,$20,$04,$40,$04,$60,$04
dcb $80,$04,$a0,$04,$c0,$04,$e0,$04
dcb $00,$05,$20,$05,$40,$05,$60,$05
dcb $80,$05,$a0,$05,$c0,$05,$e0,$05

bash and utils, 45 bytes

Inspired (well, stolen from?) @marcosm answer, here is a quite golfed down version (from his 56 bytes down to 45, shaving the -n 1, and xarg-ing into a printf %s):

shuf -i 0-16777215|xargs printf "\e[48;5;%sm "  # \e is replaced by 1 character, Escape

Excel VBA, _{131 102} 85 Bytes

Anonymous VBE immediate window function that uses a helper function (see below) to output an array of randomly colored cells to the range A1:AN40 of the activesheet object.

Note: This solution is restricted to 32-Bit installs of MS Excel (and therefore of Office as a whole) as 8^8 will not compile on 64-Bit versions of VBA

Randomize:Cells.RowHeight=48:For Each c In[A1:AN40]:c.Interior.Color=(8^8-1)*Rnd:Next

Sample Output

Previous Version

Randomize:Cells.ColumnWidth=2:For Each c In Range("A1:AN40"):c.Interior.Color=RGB(n,n,n):Next

Helper Function

Outputs a random int in the range [0,255]

Function n
n=Int(255*Rnd)
End Function

sh + ffmpeg, 52 bytes

ffplay -f rawvideo -s cif -pix_fmt rgb24 /dev/random

Does ffmpeg count as an esolang? :D

Sadly the pix_fmt is required, as ffmpeg defaults to yuv420p. That fails the "must have equal likelihood of every possible pixel color" requirement. Conveniently, cif is a shortcut for a fairly large video size that uses less space than "40x40".

Unsurprisingly, optimizing this gif with gifsicle did absolutely nothing. It's 4MiB.

GW-Basic, 47 bytes (tokenised)

0 SCREEN 7:RANDOMIZE TIMER:WHILE 1:PSET(RND*40 MOD 40,RND*40 MOD 40),RND*16 AND 15:WEND

To get it down to 47 bytes, you'll have to strip spaces and trailing zeroes and end of file character manually.

QBIC, 34 bytes

screen 12{pset(_r640|,_r480|),_r16

Unfortunately, QBIC doesn't set a SCREEN mode by default, so that eats some bytes. PSET is an illegal command in QBIC's default graphical context.

Explanation

screen 12           Set the screen to a mode supporting (colored) graphics
{                   DO until the compiler is killed by ctrl-scroll lock
pset                PSET is a QBasic command to set one pixel
(_r640|,_r480|)     it takes a set of coords (x, y) which QBIC chooses at random with _r
,_r16               and a color (1,16)

Sample output

@Anonymous found an error in QBIC's rnd() function. Fixing that gives the output below. Thanks!

Super Chip (48)?, 12 bytes

0x00FF 'enter high resolution mode (64x128 pixels)
0xA209 'set I to 0x209 (second byte of draw instruction)
0xC03F 'set register 0 to a random number from 0 to 63
0xC13F 'set register 1 to a random number from 0 to 63
0xD101 'draw a sprite. x=register 1, y=register 0, height=1
0x1204 'jump to third instruction

I'm not sure of the exact name, but I had to use this instead of normal Chip-8 because of the 40x40 pixel limitation.

Ruby, 78 Bytes

loop{print"\e[#{rand(41)};#{rand(41)}H\e[#{rand(30..37)};#{rand(1..3)}m█\e[0m"}

If you count the bytes you'll see that it's more than 78 bytes. That's because I had to replace the ASCII escape character (decimal value 27) with "\e" as stackexchange sanitizes the post. Both can be used in ruby code so the above code will work but for the purpose of golfing you can replace them with the literal escape character.

The code prints a box into the terminal at a random position from 0;0 to 40;40 with a random color.

The result will look something like this:

(result may vary depending on terminal and color scheme)

Explanation

loop {                      # Loop forever
  print "                   # Prints one long string to the terminal     
    \e[                     # Start of an ANSI escape sequence. In this case it
                            # will move the cursor
    #{rand(41)};            # Random y position
      #{rand(41)}H          # Random x position
        \e[                 # Specify the color of the following character
          #{rand(30..37)};  # Set random hue
            #{rand(1..3)}m  # Set random brightness
                    █       # The only thing that will be visible in the terminal
                    \e[0m"} # Reset the color code to keep the blocks from
                            # interfering with each other

x86 machine language (real mode) for IBM PC, 20 19 bytes

 0:       b8 12 00                mov    $0x12,%ax
 3:       31 db                   xor    %bx,%bx
 5:       cd 10                   int    $0x10
 7:       0f c7 f0                rdrand %ax
 a:       88 e1                   mov    %ah,%cl
 c:       0f c7 f2                rdrand %dx
 f:       b4 0c                   mov    $0xc,%ah
11:       eb f2                   jmp    0x5

This requires a processor with the rdrand instruction and a VGA adapter (real or emulated). The above can be copied into a boot block or MS-DOS *.COM file.

To try this out, compile the following and save the output to a file like floppy.img and boot the image on a virtual machine.

#include<stdio.h>
#include<string.h>
#include<unistd.h>
int main(){
  char buffer[ 1440*1024 ];
  memcpy( buffer, "\xb8\x12\x00\x31\xdb\xcd\x10\x0f\xc7\xf0\x88\xe1\x0f\xc7\xf2\xb4\x0c\xeb\xf2", 20 );
  memcpy( buffer + 510, "\x55\xaa", 2 );
  write( 1, buffer, sizeof buffer );
}

Processing.js, 142 bytes

for(var i=0;i<99;i++){for(var j=0;j<99;j++){fill(random(0,255),random(0,255),random(0,255),random(0,255));rect((i-1)*40,(j-1)*40,i*40,j*40);}}

TryItOnline

Bash, 104 bytes

The \es are literal escape characters.

These are pretty much translations of my Perl submission, but using bash fork bomb style syntax! Not as clever as the other bash entry that writes directly to the display I'm afraid.

:(){ printf "\e[%i;%iH\e[48;5;%im " $((RANDOM%`tput lines`)) $((RANDOM%`tput cols`)) $((RANDOM%256));:;};:

More pixels, 130 bytes

Same as my Perl answer, this uses a unicode character for the foreground and colours the background of each pixel too.

:(){ printf "\e[%i;%iH\e[48;5;%i;38;5;%im▄" $((RANDOM%`tput lines`)) $((RANDOM%`tput cols`)) $((RANDOM%256)) $((RANDOM%256));:;};:

Perl (on *nix), 69 bytes

The \x1bs are literal escape characters.

Relies on stty command and works well on OS X.

{printf"\x1b[%i;%iH\x1b[48;5;%im ",map{rand$_}`stty size`=~/\d+/g,256;redo}

Similar to other approaches, but I liked the combination of all params into one call to printf so thought I'd share. Kills my terminal.

Twice as many pixels, 83 bytes

{printf"\x1b[%i;%iH\x1b[48;5;%i;38;5;%im▄",map{rand$_}`stty size`=~/\d+/g,256,256;redo}

This approach uses a unicode block ▄ and a random foreground and background colour which gives a more square pixel. Kills my terminal too, but looks cooler.

shortC, 66 56 bytes

Dr rand()
AOZR"\e[%d;%dH\e[%d;4%dm ",r%40,r%40,r%2,r%8);

-10 bytes thanks to Dr. Rand. :P

A                                                                  main function
 O                                                                 for
  Z                                                                seed rand()
   R                                                               print
    "\e[%d;%dH                                                     coordinate placeholder string
              \e[%d;4%dm "                                         color placeholder string
                          ,rand()%40,rand()%40,rand()%2,rand()%8   fill placeholders
                                                                ); interpreter hole

No TIO link because you obviously can't print to the kind of terminal this requires online.

Ruby + ruby2d: 101+9 = 110 bytes

Uses the -rruby2d flag. 80x60 "pixel" image. Timed the module to run 100 update ticks in 2 seconds, so it theoretically replaces all pixels on the screen in under 2 minutes.

s=[]
80.times{|x|60.times{|y|s<<Square.new(x:x*8,y:y*8,size:8)}}
update{s.sample.color='random'}
show

Mathematica 112 Bytes

r:=RandomReal[];b:=⌈40r⌉;a=r&~Array~{40,40,3};Dynamic[a[[b,b]]={r,r,r};ArrayPlot[a,ColorFunction->RGBColor]]

Very straightforward, uses Dynamic around an ArrayPlot. Not terribly fast; limited by the maximum speed dynamic can update, but should fulfill the goal on most computers.

Starts out with a random 40x40 grid and recolors a random pixel one at a time. Ceiling characters are 3 bytes each, Ouch!

LOGO, 71 bytes

The only language that I know of, being not esoteric/specially designed for codegolfing, and have forever function. Any idea on the map part?

pu forever[setxy random 100 random 100 setpixel map[random 256][1 1 1]]

6502 Assembly, 92 bytes

loo: lda $fe
sta $00
lda $fe
and #$3
clc
adc #$2
sta $01
lda $fe
ldy #$0
sta ($00),y
jmp loo

Output:

Explanation:

loop: lda $fe       ; accumulator = random
      sta $00       ; store accumulator
      lda $fe       ; accumulator = random
      and #$3       ; accumulator &= 3
      clc           ; clear carry
      adc #$2       ; accumulator += 2
      sta $01       ; store accumulator
      lda $fe       ; accumulator = random
      ldy #$0       ; register Y = 0
      sta ($00),y   ; store register Y
      jmp loop      ; loop

Javascript+HTML 118 + 13 (131 bytes)

r=_=>255*Math.random()|0;setInterval('x=c.getContext`2d`;x.fillRect(r(),r(),1,1,x.fillStyle=`rgb(${[r(),r(),r()]})`)')

<canvas id=c>

• This will produce evenly distributed RGB colors. You cannot use Hex colors without proper padding as numbers like #7 is not a valid color, or #777 and #777777 are the same color (2x the odds)
• The canvas element is 300x150 by default, but I'm actually drawing on a 255x255 square, so there are off canvas pixels, so the effective area is 255x150.
• Works only on Google Chrome.

Python 3 with Pygame, 171 Bytes

import pygame as p,random as r
r=r.randint
a=p.PixelArray(p.display.set_mode((40,40)))
while(1):
    a[r(0,39),r(0,39)]=(r(0,255),r(0,255),r(0,255))
    p.display.update()

Bash + coreutils, 59 56 bytes

for((;;)){ printf "\e[48;5;`shuf -i 0-16777215 -n1`m ";}

\e[48;5;COLORm is the escape secuence to background color.

Each "pixel" has the chance to be in the [0..16777215] range every time.

JavaScript (ES7) + HTML using SVG, 129 + 10 = 139 bytes

SVG version, heavily inspired by @Octopus's <canvas> approach.

JS

r=n=>n*Math.random()|0
setInterval('s.innerHTML+=`<rect x=${r(40)} y=${r(40)} fill=#${r(2**24).toString(16)} width=1 height=1>`')

HTML

<svg id=s>

Since the Stack Snippet likes to break the script by parsing the <rect> tag, here's a CodePen.

Python 3.6 + Tkinter, 281 bytes

from tkinter import*
from random import*
from threading import*
a=randrange
x=40
d={"width":x,"height":x}
w=Tk()
c=Canvas(w,**d)
c.pack()
i=PhotoImage(**d)
c.create_image((20,20),image=i)
def r():
 while 1:i.put(f"{a(0,0xffffff):0>6f}",(a(0,x),a(0,x)))
Thread(r).start()
mainloop()

JS+HTML 162+32 (194) 124+13 (137) bytes

Thanks to Luke and other commenters for saving me lots of bytes.

r=n=>n*Math.random()|0
setInterval("b=c.getContext`2d`;b.fillStyle='#'+r(2**24).toString(16);b.fillRect(r(99),r(99),1,1)",0)

<canvas id=c>

Processing, 90 bytes

void draw(){float n=noise(millis());int i=(int)(n*9999);set(i%99,i/99,(int)(n*(-1<<24)));}

expanded and commented:

void draw(){
  float n=noise(millis());//compute PRNG value
  int i=(int)(n*9999);    //compute 99x99 pixel index
  set(i%99,i/99,          //convert index to x,y 
  (int)(n*(-1<<24)));     //PRNG ARGB color = PRNG value * 0xFFFFFFFF 
}

Ideally I could use a pixel index instead of x,y location, but Processing's pixels[] access requires loadPixels() pre and updatePixels() post, hence the use of set(). point() would work too, but has more chars and requires stroke(). The random area is actually 99x99 to save a few bytes(instead of 100x100), but that should cover 40x40 with each pixel in such an area to be replaced.

Perlin noise() is is used instead of random() to keep it more pseudo-random and a byte shorter. The value is computed once, but used twice: once for the random position, then again for the colour.

The colour is actually ARGB(00000000 to FFFFFFFF) (not RGB) (bonus points ? :D).

TI-BASIC (84+C(S)E only), 37 35 bytes

:For(A,1,5!
:For(B,1,5!
:Pxl-On(A,B,randInt(10,24
:End
:End
:prgmC //"C" is the name of this program

Due to hardware limitations, this will eventually crash, since every time a program is nested within a program in TI-BASIC, 15 KB of RAM are allocated to "keep a bookmark" in the parent program. This would run fine on a "theoretical" calculator with infinite RAM, but if we want it to run indefinitely on a real calculator, we can just wrap it in a While 1 loop for an extra 2 bytes:

:While 1
:...
:End

The TI-83 family calculators with color screens (TI 84+CE and CSE) support 15 colors. They have color codes 10 through 24. This cycles through all the pixels in a 120 by 120 (5!) square and assigns each a random color.

Result:

C on POSIX, 98 96 95 92 bytes

^{-3 thanks to Tas}

#define r rand()
f(){for(srand(time(0));printf("\e[%d;%dH\e[%d;4%dm ",r%40,r%40,r%2,r%8););}

This chooses between 16 colors (dark grey, red, green, blue, orange, cyan, purple, light grey, black, pink, light blue, yellow, light cyan, magenta, white) and prints them directly to the terminal.

Note that if your GPU is too slow, this may seem like it's updating the entire screen at once. It's actually going pixel by pixel, but C is fast.

Alternate solution that makes the colors more distinct:

f(){for(srand(time(0));printf("\e[%d;%dH\e[%d;3%dm█",rand()%40,rand()%40,rand()%2,rand()%8););}

Proof that it goes pixel by pixel (screenshot from alternate program):

Wow, that looks almost 3-dimensional...

Java 7 with JavaFX, 686 674 bytes

import javafx.scene.*;import javafx.scene.canvas.*;import javafx.scene.layout.*;public class M extends javafx.application.Application{public static void main(String[]a){launch(a);}GraphicsContext g;public M(){}public void start(javafx.stage.Stage x){BorderPane r=new BorderPane();Canvas c=new Canvas(40,40);g=c.getGraphicsContext2D();Pane p=new Pane();p.getChildren().addAll(c);r.setCenter(p);x.setScene(new Scene(r,40,40));x.show();new javafx.animation.AnimationTimer(){public void handle(long n){M.this.g.setFill(javafx.scene.paint.Color.color(Math.random(),Math.random(),Math.random()));M.this.g.fillRect((int)(Math.random()*40),(int)(Math.random()*40),1,1);}}.start();}}

Explanation:

import javafx.scene.*;import javafx.scene.canvas.*;import javafx.scene.layout.*;
                                            // Required imports

public class M extends javafx.application.Application{
                                            // The class (NOTE: The public is mandatory for JavaFX)
  public static void main(String[]a){       //  Mandatory main method
    launch(a);                              //   Call the launch of the Application
  }                                         //  End of main-method

  GraphicsContext g;                        //  GraphicsContext on class-level which we'll use in the animation

  public M(){}                              //  Empty constructor (again, mandatory for JavaFX)

  public void start(javafx.stage.Stage x){  //  Overwritten start-method of Application
    BorderPane r=new BorderPane();          //   Create a BorderPane
    Canvas c=new Canvas(40,40);             //   Create a Canvas with the minimum size
    g=c.getGraphicsContext2D();             //   Retrieve the GraphicsContext and set it to the class-level variable
    Pane p=new Pane();                      //   Create a Pane
    p.getChildren().addAll(c);              //   Add the Canvas to the Pane
    r.setCenter(p);                         //   Put it in the center (otherwise it won't show in the window)
    x.setScene(new Scene(r,40,40));         //   Create a new Scene
    x.show();                               //   And show the screen
    new javafx.animation.AnimationTimer(){  //   Create a new animation
      public void handle(long n){           //    Overwritten handle-method of this animation
        M.this.g.setFill(javafx.scene.paint.Color.color(Math.random(),Math.random(),Math.random()));
                                            //     Set a random color
        M.this.g.fillRect((int)(Math.random()*40),(int)(Math.random()*40),1,1);
                                            //     And add this color as a 1x1 pixel in a random position
      }                                     //    End of handle-method
    }.start();                              //   And start the animation
  }                                         //  End of start-method
}                                           // End of class

Output:

R, 143 138 bytes

-4 bytes thanks to user2390246

r=runif
s=sample
g=1600
x=1:40
k=hsv(r(g),r(g),r(g))
while(1){image(x,x,matrix(1:g,40),c=k)
Sys.sleep(99/g)
k[s(g,1)]=hsv(r(1),r(1),r(1))}

image makes the required 40x40 grid of rectangles with a matrix m of values (fixed to be 1:1600 in a 40x40 square), with a randomly selected color for each rectangle, k. It plots the image, waits long enough to actually render the image, then randomly changes one of the colors. Uses hsv encoding since it is a value between 0 and 1, which allows us to use runif to generate random colors.

This generates a new plot each time.

C# Console, 233 220 189 188 bytes

namespace System{using static Console;class P{static void Main(){for(var r=new Random();;){BackgroundColor=(ConsoleColor)r.Next(16);SetCursorPosition(r.Next(40),r.Next(40));Write(" ");}}}}

Uses "all" (windows) 16 console colors.

Thanks for the "feature" to be able to alias classes in C# via the using directive.

Edit #1

• Removed some spaces.

• Removed zeros from Random.Next()

• Went to namespace system{...}

Edit #2

• Minimum size of grid is 40x40

• One byte by declaring Random in for loop header

• Removed public from Main method

Edit #3

Turns out using C=Console; is not the best there is. using static Console is much like the VB.Net way to "Import" classes

I give up: TheLethalCoder made this happen

Original code for adapting window size at 207 bytes:

namespace System{using static Console;class P{static void Main(){for(var r=new Random();;){BackgroundColor=(ConsoleColor)r.Next(16);SetCursorPosition(r.Next(WindowWidth),r.Next(WindowHeight));Write(" ");}}}}

Original Image:

C#, 369 288 287 bytes

namespace System.Drawing{class P{static void Main(){var g=Graphics.FromHwnd((IntPtr)0);var w=Windows.Forms.Screen.GetBounds(Point.Empty);for(var r=new Random();;)g.FillRectangle(new SolidBrush(Color.FromArgb(r.Next(256),r.Next(256),r.Next(256))),r.Next(w.Width),r.Next(w.Height),1,1);}}}

Saved 88 bytes thanks to @CodyGray.

A full program that get's the handle to the screen and it's size and then starts randomly drawing pixels on it. Note that this might grind your graphics card to a halt when ran. Also if the screen or any control decides to repaint at any time the pixels will be lost and have to be redrawn.

Note: When running keep focus on the window as to kill it you have to either Alt+F4 or press the close button and doing so when you can't see the screen is a bit hard.

I couldn't record this working, with ScreenToGif, as that kept forcing a repaint so the pixels would get removed. However, here is a screenshot of it running after about 10-15 seconds, any longer and I think I may have ground my PC to a halt! The gap in the top right corner is where the screen forced a repaint just as I took the screenshot.

Full/Formatted version:

namespace System.Drawing
{
    class P
    {
        static void Main()
        {
            var g = Graphics.FromHdc((IntPtr)0);
            var w = Windows.Forms.Screen.GetBounds(Point.Empty);

            for (var r = new Random();;)
                g.FillRectangle(new SolidBrush(Color.FromArgb(r.Next(256), r.Next(256), r.Next(256))),
                                r.Next(w.Width), r.Next(w.Height), 1, 1);
        }
    }
}

A version for 308 227 226 bytes that only draws on the region 0-40:

namespace System.Drawing{class P{static void Main(){var g=Graphics.FromHdc((IntPtr)0);for(var r=new Random();;)g.FillRectangle(new SolidBrush(Color.FromArgb(r.Next(256),r.Next(256),r.Next(256))),r.Next(40),r.Next(40),1,1);}}}

Example output for this one:

C++ on Windows, 125 bytes

#include<Windows.h>
#include<ctime>
#define r rand()%256
int main(){for(srand(time(0));;)SetPixel(GetDC(0),r,r,RGB(r,r,r));}

Newlines necessary and included in byte count.

Loops forever, randomly picks a position between 0 and 255 (inclusive) for row and column values, assigns random R,G,B values between 0-255 (inclusive)

HTML+SVG+PHP, 245 Bytes

<?$u=$_GET;$u[rand()%40][rand()%40]=sprintf("%06x",rand()%16777216);echo'<meta http-equiv="refresh" content="0.1; url=?'.http_build_query($u).'" /><svg>';foreach($u as$x=>$a)foreach($a as$y=>$c)echo"<rect x=$x y=$y width=1 height=1 fill=#$c />";

Expanded

$u=$_GET; # Get the Url
$u[rand()%40][rand()%40]=sprintf("%06x",rand()%16777216); # Set One Value in a 2 D Array
echo'<meta http-equiv="refresh" content="0.1; url=?'.http_build_query($u).'" /><svg>'; # refresh the site after 0.1 second follow the new Get parameter
foreach($u as$x=>$a) #loop through x Coordinates as Key
  foreach($a as$y=>$c) #loop through y Coordinates as Key value is the color
    echo"<rect x=$x y=$y width=1 height=1 fill=#$c />"; #print the rects for the SVG

Example for Output without meta tag and in a greater version

<svg viewBox="0 0 40 40" width=400 height=400><rect x=11 y=39 width=1 height=1 fill=#1b372b /><rect x=11 y=7 width=1 height=1 fill=#2c55a7 /><rect x=11 y=31 width=1 height=1 fill=#97ef86 /><rect x=11 y=26 width=1 height=1 fill=#94aa0a /><rect x=11 y=4 width=1 height=1 fill=#f8bf89 /><rect x=11 y=6 width=1 height=1 fill=#266342 /><rect x=11 y=29 width=1 height=1 fill=#369d80 /><rect x=11 y=20 width=1 height=1 fill=#ccfab8 /><rect x=11 y=12 width=1 height=1 fill=#ac0273 /><rect x=13 y=25 width=1 height=1 fill=#0d95e9 /><rect x=13 y=0 width=1 height=1 fill=#d2a4cb /><rect x=13 y=37 width=1 height=1 fill=#503abe /><rect x=13 y=35 width=1 height=1 fill=#4e60ae /><rect x=13 y=30 width=1 height=1 fill=#3cdd5e /><rect x=13 y=12 width=1 height=1 fill=#60464c /><rect x=13 y=17 width=1 height=1 fill=#a3b234 /><rect x=13 y=3 width=1 height=1 fill=#48e937 /><rect x=13 y=20 width=1 height=1 fill=#58bb78 /><rect x=13 y=4 width=1 height=1 fill=#5c61e6 /><rect x=13 y=10 width=1 height=1 fill=#758613 /><rect x=13 y=21 width=1 height=1 fill=#9b3a09 /><rect x=13 y=28 width=1 height=1 fill=#6c6b3b /><rect x=13 y=32 width=1 height=1 fill=#9b3a0f /><rect x=13 y=14 width=1 height=1 fill=#0c9bcc /><rect x=38 y=34 width=1 height=1 fill=#a3a65d /><rect x=38 y=23 width=1 height=1 fill=#c4441a /><rect x=38 y=25 width=1 height=1 fill=#cec692 /><rect x=38 y=39 width=1 height=1 fill=#535401 /><rect x=38 y=30 width=1 height=1 fill=#21371a /><rect x=38 y=26 width=1 height=1 fill=#7560a4 /><rect x=38 y=33 width=1 height=1 fill=#f31f34 /><rect x=38 y=9 width=1 height=1 fill=#3fce3f /><rect x=38 y=13 width=1 height=1 fill=#78cab8 /><rect x=3 y=39 width=1 height=1 fill=#c6cf06 /><rect x=3 y=26 width=1 height=1 fill=#d7fc94 /><rect x=3 y=31 width=1 height=1 fill=#048791 /><rect x=3 y=19 width=1 height=1 fill=#140371 /><rect x=3 y=12 width=1 height=1 fill=#6e7e7a /><rect x=3 y=21 width=1 height=1 fill=#f917da /><rect x=3 y=36 width=1 height=1 fill=#00d5d7 /><rect x=3 y=24 width=1 height=1 fill=#00f119 /><rect x=34 y=15 width=1 height=1 fill=#e39bd7 /><rect x=34 y=1 width=1 height=1 fill=#c1c1b8 /><rect x=34 y=36 width=1 height=1 fill=#0d15d5 /><rect x=34 y=29 width=1 height=1 fill=#d15f57 /><rect x=34 y=11 width=1 height=1 fill=#6f73b9 /><rect x=34 y=33 width=1 height=1 fill=#93ce78 /><rect x=34 y=16 width=1 height=1 fill=#ddd7bd /><rect x=34 y=14 width=1 height=1 fill=#73caa6 /><rect x=34 y=28 width=1 height=1 fill=#972d89 /><rect x=34 y=31 width=1 height=1 fill=#27e401 /><rect x=34 y=10 width=1 height=1 fill=#559d6d /><rect x=34 y=22 width=1 height=1 fill=#170bc2 /><rect x=30 y=13 width=1 height=1 fill=#a9ac0d /><rect x=30 y=4 width=1 height=1 fill=#3d9530 /><rect x=30 y=10 width=1 height=1 fill=#67b434 /><rect x=30 y=15 width=1 height=1 fill=#54930a /><rect x=30 y=11 width=1 height=1 fill=#8ce15b /><rect x=30 y=7 width=1 height=1 fill=#ddf53d /><rect x=30 y=32 width=1 height=1 fill=#04de14 /><rect x=30 y=19 width=1 height=1 fill=#f52098 /><rect x=30 y=22 width=1 height=1 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Processing, 112 bytes

void setup(){size(40,40);}void draw(){stroke(random(255),random(255),random(255));point(random(40),random(40));}

I can't guarantee that every pixel is replaced every 3 minutes, but looking at it it appears to be doing so. At least the odds of it missing a pixel, out of 1600 total, updating a random one 30x per second, totaling 5400 updates per 3 minutes, makes it unlikely that one would be missed.

Ungolfed:

The program is really straightforward. Open a window at 40x40 pixels, and every frame (default 30 per second) get a random color, and draw a point at a random coordinate between 0 and the parameter. 40 for pixel coordinates, 255 for colors.

void setup()
{
  size(40,40);
}

void draw()
{
  stroke(random(255),random(255),random(255));
  point(random(40),random(40));
}

Python, 162 bytes

Uses OpenCV library to show the RGB array. Pair of bytes can be saved if define smaller array or a square array.
Note: imshow and waitkey methods are from cv2 module; zeros and random.randint are from numpy module.

from cv2 import *
from numpy import *
h=200
w=200
c=zeros((h,w,3),"u1")
R=random.randint
while 1:
    c[R(h),R(w)]=R(256,size=3)
    imshow("",c)
    waitKey(1)

JavaScript using Canvas 340 316 324 bytes

function r(t,e){return Math.floor(e*Math.random()+t)}function f(){x.fillStyle="rgba("+r(1,255)+","+r(1,255)+","+r(1,255)+", 1)",x.fillRect(r(0,40),r(0,40),1,1)}c=document.createElement("canvas"),c.width=40,c.height=40,x=c.getContext("2d"),document.getElementsByTagName("body")[0].appendChild(c),c.interval=setInterval(f,1);

full version

Python, 133 bytes

I'm not quite sure if this fits the specs, because it's on a canvas in a 40x40 area.

from turtle import*
from random import*
ht()
up()
speed(0)
R=randint
while 1:goto(R(0,39),R(0,39));dot(1,eval('('+'R(0,255),'*3+')'))

Try it online - version without eval, which doesn't work in Trinket

MATLAB, 56 bytes

x=rand(40,40,3);while imagesc(x),x(randi(4800))=rand;end

Output looks like the image below. One "pixel" changes at a time, and only one of the RGB-colors changes.

Why? The colors in MATLAB are represented as a 3D-matrix, one layer for R,G and B. The code above changes only one of the layers per iteration. All pixels and all layers can be changed, so if you wait a bit all colors are equally possible in all positions.

Add pause(t) inside the loop to pause t seconds between each image.

You must stop it with Ctrl+C.