Galton box animation

(Redirected from Galton Box)
Galton box animation
You are encouraged to solve this task according to the task description, using any language you may know.

A   Galton device   Sir Francis Galton's device   is also known as a   bean machine,   a   Galton Board,   or a   quincunx.

Description of operation

In a Galton box, there are a set of pins arranged in a triangular pattern.   A number of balls are dropped so that they fall in line with the top pin, deflecting to the left or the right of the pin.   The ball continues to fall to the left or right of lower pins before arriving at one of the collection points between and to the sides of the bottom row of pins.

Eventually the balls are collected into bins at the bottom   (as shown in the image),   the ball column heights in the bins approximate a   bell curve.   Overlaying   Pascal's triangle   onto the pins shows the number of different paths that can be taken to get to each bin.

Generate an animated simulation of a Galton device.

•   The box should have at least 5 pins on the bottom row.
•   A solution can use graphics or ASCII animation.
•   Provide a sample of the output/display such as a screenshot.
•   There can be one or more balls in flight at the same time.
•   If multiple balls are in flight, ensure they don't interfere with each other.
•   A solution should allow users to specify the number of balls, or it should run until full or a preset limit.
•   Optionally,   display the number of balls.

AutoHotkey

Uses an edit box for the (text based) animation

```AutoTrim Off
; User settings
bottompegs := 6
SleepTime  := 200
fallspace  := 30

; create the board
out := (pad2 := Space(bottompegs*2+1)) "`n"
Loop % bottompegs
{
out .= Space(bottompegs-A_Index+1)
Loop % A_Index
out .= "* "
out .= Space(bottompegs-A_Index+1) . "`n"
}
StringTrimRight, strboard, out, 1 ; remove last newline
Loop % fallspace-1
strboard .= "`n"
Loop % bottompegs*2+1
strboard .= "="

; Create Gui
Gui Font, , Consolas
Gui -Caption
Gui Margin, 0, 0
Gui, Add, edit, -VScroll vE, % strboard
Gui Show
Loop
{
ballX := bottompegs+1, BallY := 1
strboard := ChangeChar(strboard, BallX, ballY, "O")
GuiControl,, E, % strboard
sleep SleepTime
; Make ball fall and bounce
Loop % bottompegs
{
strboard := ChangeChar(strboard, BallX, BallY, " ")
ballY += 1
; MsgBox % ballX ", " ballY
GuiControl,, E, % strboard := ChangeChar(strboard, ballX, ballY, "O")
sleep SleepTime
}
; now fall to the bottom
While GetChar(strboard, BallX, BallY+1) = A_Space
{
strboard := ChangeChar(strboard, BallX, BallY, " ")
BallY += 1
strboard := ChangeChar(strboard, BallX, BallY, "O")
GuiControl,, E, % strboard
sleep SleepTime
}
}
~Esc::
GuiClose:
ExitApp

Space(n){
If n
return " " Space(n-1)
return ""
}
Random, n, 3, 4
return (n=3 ? -1 : 1)
}

GetChar(s, x, y){
Loop Parse, s, `n
if (A_Index = y)
return SubStr(A_LoopField, x, 1)
}
ChangeChar(s, x, y, c){
Loop Parse, s, `n
{
If (A_Index = y)
{
Loop Parse, A_LoopField
If (A_Index = x)
out .= c
else    out .= A_LoopField
}
else out .= A_LoopField
out .= "`n"
}
StringTrimRight, out, out, 1 ; removes the last newline
return out
}
```

While the number of pegs, and falling space are configurable, here's output shortly after starting one configuration:

```
*
* *O
* * *
* * * *
* * * * *
* * * * * *

O
O O
O O O O
O O O O O
=============```

BASIC256

```graphsize 150,125
fastgraphics
color black
rect 0,0,graphwidth,graphheight
refresh

N = 10		# number of balls
M = 5		# number of pins in last row
dim ball(N,5)	# (pos_x to center, level, x, y, direction}
dim cnt(M+1)

slow = 0.3
CX = graphwidth/2 : CY = graphheight/2
iters = 0

# Draw pins
for i = 1 to M
for j = 1 to i
color purple
stamp CX+dx,y,1.0,diamond
color darkpurple
stamp CX+dx,y,0.6,diamond
next j
next i
gosub saverefresh

R = 0 : C = 0
font "Tahoma",10,50
do
# Release ball
if R<N then
R = R + 1
ball[R-1,2] = CX : ball[R-1,3] = rad*(1-stepx[?]) : ball[R-1,4] = 0
# How many balls are released
color black
text 5,5,(R-1)+" balls"
color green
text 5,5,(R)+" balls"
end if
# Animate balls on this step
for it = 0 to stepx[?]-1
for b = 0 to R-1
gosub moveball
next b
gosub saverefresh
pause slow/stepx[?]
next it
# Where to go on the next step?
for b = 0 to R-1
ball[b,1] = ball[b,1] + 1
if ball[b,1]<=M then
if rand>=0.5 then
ball[b,4] = 1
else
ball[b,4] = -1
end if
ball[b,0] = ball[b,0] + ball[b,4]
else
if ball[b,4]<>0 then
gosub eraseball
i = (ball[b,0]+M)/2
cnt[i] = cnt[i] + 1
ball[b,4] = 0
C = C + 1
end if
end if
next b
# Draw counter
color green
for j = 0 to M
next j
gosub saverefresh
until C >= N
end

moveball:
if ball[b,1]>M then return
gosub eraseball
if ball[b,4]<>0.0 then
ball[b,2] = ball[b,2]+ball[b,4]*stepx[it]
ball[b,3] = ball[b,3]+stepy[it]
else
end if
gosub drawball

drawball:
color darkgreen
color green
return

eraseball:
color black
return

saverefresh:
num\$ = string(iters)
for k = 1 to 4-length(num\$)
num\$ = "0"+num\$
next k
imgsave num\$+"-Galton_box_BASIC-256.png", "PNG"
iters = iters + 1
refresh
return```

BBC BASIC

```      maxBalls% = 10
DIM ballX%(maxBalls%), ballY%(maxBalls%)

VDU 23,22,180;400;8,16,16,128
ORIGIN 180,0
OFF

REM Draw the pins:
GCOL 9
FOR row% = 1 TO 7
FOR col% = 1 TO row%
CIRCLE FILL 40*col% - 20*row% - 20, 800 - 40*row%, 12
NEXT
NEXT row%

REM Animate
last% = 0
tick% = 0
GCOL 3,3
REPEAT
IF RND(10) = 5 IF (tick% - last%) > 10 THEN
FOR ball% = 1 TO maxBalls%
IF ballY%(ball%) = 0 THEN
ballX%(ball%) = 0
ballY%(ball%) = 800
last% = tick%
EXIT FOR
ENDIF
NEXT
ENDIF
FOR ball% = 1 TO maxBalls%
IF ballY%(ball%) CIRCLE FILL ballX%(ball%), ballY%(ball%), 12
IF POINT(ballX%(ball%),ballY%(ball%)-10) = 12 OR ballY%(ball%) < 12 THEN
IF ballY%(ball%) > 500 END
ballY%(ball%) = 0
ENDIF
NEXT
WAIT 2
FOR ball% = 1 TO maxBalls%
IF ballY%(ball%) THEN
CIRCLE FILL ballX%(ball%), ballY%(ball%), 12
ballY%(ball%) -= 4
IF POINT(ballX%(ball%),ballY%(ball%)-10) = 9 THEN
ballX%(ball%) += 40 * (RND(2) - 1.5)
ENDIF
ENDIF
NEXT
tick% += 1
UNTIL FALSE
```

C

```#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define BALLS 1024
int n, w, h = 45, *x, *y, cnt = 0;
char *b;

#define B(y, x) b[(y)*w + x]
#define C(y, x) ' ' == b[(y)*w + x]
#define V(i) B(y[i], x[i])
inline int rnd(int a) { return (rand()/(RAND_MAX/a))%a; }

void show_board()
{
int i, j;
for (puts("\033[H"), i = 0; i < h; i++, putchar('\n'))
for (j = 0; j < w; j++, putchar(' '))
printf(B(i, j) == '*' ?
C(i - 1, j) ? "\033[32m%c\033[m" :
"\033[31m%c\033[m" : "%c", B(i, j));
}

void init()
{
int i, j;
puts("\033[H\033[J");
b = malloc(w * h);
memset(b, ' ', w * h);

x = malloc(sizeof(int) * BALLS * 2);
y = x + BALLS;

for (i = 0; i < n; i++)
for (j = -i; j <= i; j += 2)
B(2 * i+2, j + w/2) = '*';
srand(time(0));
}

void move(int idx)
{
int xx = x[idx], yy = y[idx], c, kill = 0, sl = 3, o = 0;

if (yy < 0) return;
if (yy == h - 1) { y[idx] = -1; return; }

switch(c = B(yy + 1, xx)) {
case ' ':	yy++; break;
case '*':	sl = 1;
default:	if (xx < w - 1 && C(yy, xx + 1) && C(yy + 1, xx + 1))
if (!rnd(sl++)) o = 1;
if (xx && C(yy, xx - 1) && C(yy + 1, xx - 1))
if (!rnd(sl++)) o = -1;
if (!o) kill = 1;
xx += o;
}

c = V(idx); V(idx) = ' ';
idx[y] = yy, idx[x] = xx;
B(yy, xx) = c;
if (kill) idx[y] = -1;
}

int run(void)
{
static int step = 0;
int i;
for (i = 0; i < cnt; i++) move(i);
if (2 == ++step && cnt < BALLS) {
step = 0;
x[cnt] = w/2;
y[cnt] = 0;
if (V(cnt) != ' ') return 0;
V(cnt) = rnd(80) + 43;
cnt++;
}
return 1;
}

int main(int c, char **v)
{
if (c < 2 || (n = atoi(v[1])) <= 3) n = 5;
if (n >= 20) n = 20;
w = n * 2 + 1;
init();

do { show_board(), usleep(60000); } while (run());

return 0;
}
```

Sample out put at begining of a run:

```          *

*   *

*   *   *

*   *   *   *

*   *   *   *   *
```

C++

Windows GDI version.

```#include "stdafx.h"
#include <windows.h>
#include <stdlib.h>

const int BMP_WID = 410, BMP_HEI = 230, MAX_BALLS = 120;

class myBitmap {
public:
myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
~myBitmap() {
DeleteObject( pen ); DeleteObject( brush );
DeleteDC( hdc ); DeleteObject( bmp );
}
bool create( int w, int h ) {
BITMAPINFO bi;
ZeroMemory( &bi, sizeof( bi ) );
bi.bmiHeader.biBitCount    = sizeof( DWORD ) * 8;

HDC dc = GetDC( GetConsoleWindow() );
bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
if( !bmp ) return false;
hdc = CreateCompatibleDC( dc );
SelectObject( hdc, bmp );
ReleaseDC( GetConsoleWindow(), dc );
width = w; height = h;
return true;
}
void clear( BYTE clr = 0 ) {
memset( pBits, clr, width * height * sizeof( DWORD ) );
}
void setBrushColor( DWORD bClr ) {
if( brush ) DeleteObject( brush );
brush = CreateSolidBrush( bClr );
SelectObject( hdc, brush );
}
void setPenColor( DWORD c ) {
clr = c; createPen();
}
void setPenWidth( int w ) {
wid = w; createPen();
}
HDC getDC() const     { return hdc; }
int getWidth() const  { return width; }
int getHeight() const { return height; }
private:
void createPen() {
if( pen ) DeleteObject( pen );
pen = CreatePen( PS_SOLID, wid, clr );
SelectObject( hdc, pen );
}
HBITMAP bmp;
HDC     hdc;
HPEN    pen;
HBRUSH  brush;
void    *pBits;
int     width, height, wid;
DWORD   clr;
};
class point {
public:
int x; float y;
void set( int a, float b ) { x = a; y = b; }
};
typedef struct {
point position, offset;
bool alive, start;
}ball;
class galton {
public :
galton() {
bmp.create( BMP_WID, BMP_HEI );
initialize();
}
void setHWND( HWND hwnd ) { _hwnd = hwnd; }
void simulate() {
draw(); update(); Sleep( 1 );
}
private:
void draw() {
bmp.clear();
bmp.setPenColor( RGB( 0, 255, 0 ) );
bmp.setBrushColor( RGB( 0, 255, 0 ) );
int xx, yy;
for( int y = 3; y < 14; y++ ) {
yy = 10 * y;
for( int x = 0; x < 41; x++ ) {
xx = 10 * x;
if( pins[y][x] )
Rectangle( bmp.getDC(), xx - 3, yy - 3, xx + 3, yy + 3 );
}
}
bmp.setPenColor( RGB( 255, 0, 0 ) );
bmp.setBrushColor( RGB( 255, 0, 0 ) );
ball* b;
for( int x = 0; x < MAX_BALLS; x++ ) {
b = &balls[x];
if( b->alive )
Rectangle( bmp.getDC(), static_cast<int>( b->position.x - 3 ), static_cast<int>( b->position.y - 3 ),
static_cast<int>( b->position.x + 3 ), static_cast<int>( b->position.y + 3 ) );
}
for( int x = 0; x < 70; x++ ) {
if( cols[x] > 0 ) {
xx = 10 * x;
Rectangle( bmp.getDC(), xx - 3, 160, xx + 3, 160 + cols[x] );
}
}
HDC dc = GetDC( _hwnd );
BitBlt( dc, 0, 0, BMP_WID, BMP_HEI, bmp.getDC(), 0, 0, SRCCOPY );
ReleaseDC( _hwnd, dc );
}
void update() {
ball* b;
for( int x = 0; x < MAX_BALLS; x++ ) {
b = &balls[x];
if( b->alive ) {
b->position.x += b->offset.x; b->position.y += b->offset.y;
if( x < MAX_BALLS - 1 && !b->start && b->position.y > 50.0f ) {
b->start = true;
balls[x + 1].alive = true;
}
int c = ( int )b->position.x, d = ( int )b->position.y + 6;
if( d > 10 || d < 41 ) {
if( pins[d / 10][c / 10] ) {
if( rand() % 30 < 15 ) b->position.x -= 10;
else b->position.x += 10;
}
}
if( b->position.y > 160 ) {
b->alive = false;
cols[c / 10] += 1;
}
}
}
}
void initialize() {
for( int x = 0; x < MAX_BALLS; x++ ) {
balls[x].position.set( 200, -10 );
balls[x].offset.set( 0, 0.5f );
balls[x].alive = balls[x].start = false;
}
balls[0].alive = true;
for( int x = 0; x < 70; x++ )
cols[x] = 0;
for( int y = 0; y < 70; y++ )
for( int x = 0; x < 41; x++ )
pins[x][y] = false;
int p;
for( int y = 0; y < 11; y++ ) {
p = ( 41 / 2 ) - y;
for( int z = 0; z < y + 1; z++ ) {
pins[3 + y][p] = true;
p += 2;
}
}
}
myBitmap bmp;
HWND _hwnd;
bool pins[70][40];
ball balls[MAX_BALLS];
int cols[70];
};
class wnd {
public:
int wnd::Run( HINSTANCE hInst ) {
_hInst = hInst;
_hwnd = InitAll();
_gtn.setHWND( _hwnd );
ShowWindow( _hwnd, SW_SHOW );
UpdateWindow( _hwnd );
MSG msg;
ZeroMemory( &msg, sizeof( msg ) );
while( msg.message != WM_QUIT ) {
if( PeekMessage( &msg, NULL, 0, 0, PM_REMOVE ) != 0 ) {
TranslateMessage( &msg );
DispatchMessage( &msg );
} else _gtn.simulate();
}
return UnregisterClass( "_GALTON_", _hInst );
}
private:
static int WINAPI wnd::WndProc( HWND hWnd, UINT msg, WPARAM wParam, LPARAM lParam ) {
switch( msg ) {
case WM_DESTROY: PostQuitMessage( 0 ); break;
default:
return static_cast<int>( DefWindowProc( hWnd, msg, wParam, lParam ) );
}
return 0;
}
HWND InitAll() {
WNDCLASSEX wcex;
ZeroMemory( &wcex, sizeof( wcex ) );
wcex.cbSize           = sizeof( WNDCLASSEX );
wcex.style           = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc   = ( WNDPROC )WndProc;
wcex.hInstance     = _hInst;
wcex.hCursor       = LoadCursor( NULL, IDC_ARROW );
wcex.hbrBackground = ( HBRUSH )( COLOR_WINDOW + 1 );
wcex.lpszClassName = "_GALTON_";
RegisterClassEx( &wcex );
RECT rc;
SetRect( &rc, 0, 0, BMP_WID, BMP_HEI );
return CreateWindow( "_GALTON_", ".: Galton Box -- PJorente :.", WS_SYSMENU, CW_USEDEFAULT, 0, rc.right - rc.left, rc.bottom - rc.top, NULL, NULL, _hInst, NULL );
}
HINSTANCE _hInst;
HWND      _hwnd;
galton    _gtn;
};
int APIENTRY WinMain( HINSTANCE hInstance, HINSTANCE hPrevInstance, LPTSTR lpCmdLine, int nCmdShow ) {
srand( GetTickCount() );
wnd myWnd;
return myWnd.Run( hInstance );
}
```

Clojure

```(def n 8)
(def balls* (atom [{:x n :y 0}]))
(def board* (atom (vec (repeat (inc n) (vec (repeat (inc (* 2 n)) " "))))))
(doseq [y (range (inc n))
i (range y)]
(swap! board* assoc-in [y (+ (- n y) (* 2 i) 1)] "^"))
(def histogram* (atom (vec (repeat (inc (* 2 n)) 0))))

(loop [frame 0]
(print "\033[0;0f\033[2J")
(doseq [row @board*] (println (apply str row)))
(let [depth (inc (apply max (map #(quot % 8) @histogram*)))]
(dotimes [y depth]
(doseq [i @histogram*]
(print (nth " ▁▂▃▄▅▆▇█" (min 8 (max 0 (- i (* (- depth y 1) 8)))))))
(print "\n")))
(println "\n")
(flush)
(doseq [[i {:keys [x y]}] (map-indexed vector @balls*)]
(swap! board* assoc-in [y x] " ")
(let [[new-x new-y] [(if (< 0.5 (rand)) (inc x) (dec x)) (inc y)]]
(if (> new-y n)
(do (swap! histogram* update x inc)
(swap! balls* assoc i {:x n :y 0}))
(do (swap! board* assoc-in [new-y new-x] "*")
(swap! balls* assoc i {:x new-x :y new-y})))))
(when (< (count @balls*) n) (swap! balls* conj {:x n :y 0}))
(when (< frame 200) (recur (inc frame))))
```

Sample output:

```
^*
^*^
^ ^ ^
^ ^ ^*^
^*^ ^ ^ ^
^ ^ ^*^ ^ ^
^ ^ ^ ^*^ ^ ^
^ ^ ^*^ ^ ^ ^ ^
▅ ▅
█ █ ▂
█ █ █
▃ █ █ █
█ █ █ █ █
▁ ▇ █ █ █ █ █ ▃ ▁
```

D

To keep the code simpler some corner cases are ignored.

```import std.stdio, std.algorithm, std.random, std.array;

enum int boxW = 41, boxH = 37; // Galton box width and height.
enum int pinsBaseW = 19;       // Pins triangle base size.
enum int nMaxBalls = 55;       // Number of balls.

static assert(boxW >= 2 && boxH >= 2);
static assert((boxW - 4) >= (pinsBaseW * 2 - 1));
static assert((boxH - 3) >= pinsBaseW);
enum centerH = pinsBaseW + (boxW - (pinsBaseW * 2 - 1)) / 2 - 1;

enum Cell : char { empty  = ' ',
ball   = 'o',
wall   = '|',
corner = '+',
floor  = '-',
pin    = '.' }

Cell[boxW][boxH] box; // Galton box. Will be printed upside-down.

struct Ball {
int x, y; // Position.

this(in int x_, in int y_) nothrow @safe @nogc
in {
assert(box[y_][x_] == Cell.empty);
} body {
this.x = x_;
this.y = y_;
box[y][x] = Cell.ball;
}

nothrow const @safe @nogc invariant {
assert(x >= 0 && x < boxW && y >= 0 && y < boxH);
assert(box[y][x] == Cell.ball);
}

void doStep() {
if (y <= 0)
return; // Reached the bottom of the box.

final switch (box[y - 1][x]) with (Cell) {
case empty:
box[y][x] = Cell.empty;
y--;
box[y][x] = Cell.ball;
break;
case ball, wall, corner, floor:
// It's frozen. (It always piles on other balls).
break;
case pin:
box[y][x] = Cell.empty;
y--;
if (box[y][x - 1] == Cell.empty && box[y][x + 1] == Cell.empty) {
x += uniform(0, 2) * 2 - 1;
box[y][x] = Cell.ball;
return;
} else if (box[y][x - 1] == Cell.empty) {
x++;
} else {
x--;
}
box[y][x] = Cell.ball;
break;
}
}
}

void initializeBox() {
// Set ceiling and floor:
box[0][] = Cell.corner ~ [Cell.floor].replicate(boxW - 2) ~ Cell.corner;
box[\$ - 1][] = box[0][];

// Set walls:
foreach (immutable r; 1 .. boxH - 1)
box[r][0] = box[r][\$ - 1] = Cell.wall;

// Set pins:
foreach (immutable nPins; 1 .. pinsBaseW + 1)
foreach (pin; 0 .. nPins)
box[boxH - 2 - nPins][centerH + 1 - nPins + pin * 2] = Cell.pin;
}

void drawBox() {
foreach_reverse (const ref row; box)
writefln("%(%c%)", row);
}

void main() {
initializeBox;
Ball[] balls;

foreach (const i; 0 .. nMaxBalls + boxH) {
writefln("\nStep %d:", i);
if (i < nMaxBalls)
balls ~= Ball(centerH, boxH - 2); // Add ball.
drawBox;

// Next step for the simulation.
// Frozen balls are kept in balls array for simplicity.
foreach (ref b; balls)
b.doStep;
}
}
```
Output:
```Step 0:
+---------------------------------------+
|                   o                   |
|                   .                   |
|                  . .                  |
|                 . . .                 |
|                . . . .                |
|               . . . . .               |
|              . . . . . .              |
|             . . . . . . .             |
|            . . . . . . . .            |
|           . . . . . . . . .           |
|          . . . . . . . . . .          |
|         . . . . . . . . . . .         |
|        . . . . . . . . . . . .        |
|       . . . . . . . . . . . . .       |
|      . . . . . . . . . . . . . .      |
|     . . . . . . . . . . . . . . .     |
|    . . . . . . . . . . . . . . . .    |
|   . . . . . . . . . . . . . . . . .   |
|  . . . . . . . . . . . . . . . . . .  |
| . . . . . . . . . . . . . . . . . . . |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
|                                       |
+---------------------------------------+

...

Step 39:
+---------------------------------------+
|                   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                |
+---------------------------------------+

...

Step 91:
+---------------------------------------+
|                                       |
|                   .                   |
|                  . .                  |
|                 . . .                 |
|                . . . .                |
|               . . . . .               |
|              . . . . . .              |
|             . . . . . . .             |
|            . . . . . . . .            |
|           . . . . . . . . .           |
|          . . . . . . . . . .          |
|         . . . . . . . . . . .         |
|        . . . . . . . . . . . .        |
|       . . . . . . . . . . . . .       |
|      . . . . . . . . . . . . . .      |
|     . . . . . . . . . . . . . . .     |
|    . . . . . . . . . . . . . . . .    |
|   . . . . . . . . . . . . . . . . .   |
|  . . . . . . . . . . . . . . . . . .  |
| . . . . . . . . . . . . . . . . . . . |
|                                       |
|                                       |
|                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          |
+---------------------------------------+```

EasyLang

```sys topleft
#
proc drawpins . .
for i to 9
for j to i
move (15 - i) * 3 + j * 6 i * 6 + 2
circle 0.7
.
.
.
color 555
drawpins
background -1
#
len box[] 10
len x[] 10
len y[] 10
#
proc showbox . .
for i to 10
x = i * 6 + 15
for j to box[i]
move x 100 - j * 4 + 2
circle 2
.
.
.
proc init . .
for i to 10
box[i] = 0
x[i] = 0
.
.
#
color 543
on timer
if busy = 0 and randint 4 = 1
busy = 1
for i to 10
if x[i] = 0
x[i] = 48
y[i] = 2
break 1
.
.
else
busy = 0
.
clear
showbox
for i to 10
x = x[i]
if x > 0
if y[i] <= 56
y[i] += 2
if y[i] mod 6 = 2
x += 3 * (randint 2 * 2 - 3)
x[i] = x
.
else
idx = (x - 15) / 6
y[i] += 4
if y[i] >= 96 - box[idx] * 4
x[i] = 0
box[idx] += 1
if box[idx] > 10
init
break 1
.
.
.
move x y[i]
circle 2
.
.
timer 0.1
.
timer 0```

Elm

```import Html.App exposing (program)
import Time exposing (Time, every, millisecond)
import Color exposing (Color, black, red, blue, green)
import Collage exposing (collage)
import Collage exposing (collage,polygon, filled, move, Form, circle)
import Element exposing (toHtml)
import Html exposing (Attribute, Html, text, div, input, button)
import Html.Attributes as A exposing (type', min, placeholder, value, style, disabled)
import Html.Events exposing (onInput, targetValue, onClick)
import Dict exposing (Dict, get, insert)
import String exposing (toInt)
import Result exposing (withDefault)
import Random.Pcg as Random exposing (Seed, bool, initialSeed, independentSeed, step, map)

width = 500
height = 600
hscale = 10.0
vscale = hscale * 2
margin = 30
levelCount = 12

type State = InBox Int Int Seed | Falling Int Float Float Float | Landed Int Float

type Coin = Coin State Color

colorCycle : Int -> Color
colorCycle i =
case i % 3 of
0 -> red
1 -> blue
_ -> green

initCoin : Int -> Seed -> Coin
initCoin indx seed = Coin (InBox 0 0 seed) (colorCycle indx)

drawCoin : Coin -> Form
drawCoin (Coin state color) =
let dropLevel = toFloat (height//2 - margin)
(level, shift, distance) =
case state of
InBox level shift seed -> (level, shift, 0)
Falling shift distance _ _-> (levelCount, shift, distance)
Landed shift distance -> (levelCount, shift, distance)
position =
(             hscale * toFloat shift
, dropLevel - vscale * (toFloat level) - distance + radius / 2.0)

in radius |> circle |> filled color |> move position

drawGaltonBox : List Form
drawGaltonBox =
let levels = [0..levelCount-1]

-- doubles :
-- [0,2,4,6,8...]
doubles = List.map (\n -> 2 * n) levels

-- sequences :
-- [[0], [0,2], [0,2,4], [0,2,4,6], [0,2,4,6,8],...]
sequences = case List.tail (List.scanl (::) [] (doubles)) of
Nothing -> []
Just ls -> ls

-- galtonCoords :
-- [                            (0,0),
--                       (-1,1),      (1,1),
--                (-2,2),       (0,2),      (2,2),
--         (-3,3),       (-1,3),      (1,3),      (3,3),
--  (-4,4),       (-2,4),       (0,4),      (2,4),      (4,4), ...]
galtonCoords =
List.map2
(\ls level -> List.map (\n -> (n - level, level)) ls)
sequences
levels
|> List.concat

peg = polygon [(0,0), (-4, -8), (4, -8)] |> filled black

apex = toFloat (height//2 - margin)

in List.map (\(x,y) -> move (hscale*toFloat x,  apex - vscale*toFloat y) peg) galtonCoords

coinsInBin : Int -> Dict Int Int -> Int
coinsInBin binNumber bins =
case get binNumber bins of
Nothing -> 0
Just n -> n

addToBins : Int -> Dict Int Int -> Dict Int Int
insert binNumber (coinsInBin binNumber bins + 1) bins

updateCoin : (Coin, Dict Int Int) -> (Coin, Dict Int Int)
updateCoin (Coin state color as coin, bins) =
case state of
InBox level shift seed ->
let deltaShift = map (\b -> if b then 1 else -1) bool
(delta, newSeed) = step deltaShift seed
newShift = shift+delta
newLevel = (level)+1
in if (newLevel < levelCount) then
(Coin (InBox newLevel newShift newSeed) color, bins)
else -- transition to falling
let maxDrop = toFloat (height - 2 * margin) - toFloat (levelCount) * vscale
floor = maxDrop - toFloat (coinsInBin newShift bins) * (radius*2 + 1)
in (Coin (Falling newShift -((vscale)/2.0) 10 floor) color, addToBins newShift bins)

Falling shift distance velocity floor ->
let newDistance = distance + velocity
in if (newDistance < floor) then
(Coin (Falling shift newDistance (velocity + 1) floor) color, bins)
else -- transtion to landed
(Coin (Landed shift floor) color, bins)

Landed _ _ -> (coin, bins) -- unchanged

type alias Model =
{ coins : List Coin
, bins : Dict Int Int
, count : Int
, started : Bool
, seedInitialized : Bool
, seed : Seed
}

init : (Model, Cmd Msg)
init =
( { coins = []
, bins = Dict.empty
, count = 0
, started = False
, seedInitialized = False
, seed = initialSeed 45 -- This will not get used.  Actual seed used is time dependent and set when the first coin drops.
}, Cmd.none)

type Msg = Drop Time | Tick Time | SetCount String | Go

update : Msg -> Model -> (Model, Cmd Msg)
update action model =
case action of
Go ->
({model | started = model.count > 0}, Cmd.none)

SetCount countString ->
({ model | count = toInt countString |> withDefault 0 }, Cmd.none)

Drop t ->
if (model.started && model.count > 0) then
let newcount = model.count - 1
seed' =  if model.seedInitialized then model.seed else initialSeed (truncate t)
(seed'', coinSeed) = step independentSeed seed'
in ({ model
| coins = initCoin (truncate t) coinSeed :: model.coins
, count = newcount
, started = newcount > 0
, seedInitialized = True
, seed = seed''}, Cmd.none)
else
(model, Cmd.none)

Tick _ ->
-- foldr to execute update, append to coins, replace bins
let (updatedCoins, updatedBins) =
List.foldr (\coin (coinList, bins) ->
let (updatedCoin, updatedBins) = updateCoin (coin, bins)
in (updatedCoin :: coinList, updatedBins))
([], model.bins)
model.coins
in ({ model | coins = updatedCoins, bins = updatedBins}, Cmd.none)

view : Model -> Html Msg
view model =
div []
[ input
[ placeholder "How many?"
, let showString = if model.count > 0 then model.count |> toString else ""
in value showString
, onInput SetCount
, disabled model.started
, style [ ("height", "20px") ]
, type' "number"
, A.min "1"
]
[]

, button
[ onClick Go
, disabled model.started
, style [ ("height", "20px") ]
]
[ Html.text "GO!" ]

, let coinForms = (List.map (drawCoin) model.coins)
in collage width height (coinForms ++ drawGaltonBox) |> toHtml
]

subscriptions model =
Sub.batch
[ every (40*millisecond) Tick
, every (200*millisecond) Drop
]

main =
program
{ init = init
, view = view
, update = update
, subscriptions = subscriptions
}
```

Link to live demo: http://dc25.github.io/galtonBoxAnimationElm/ . Follow the link, enter a number and press the GO button.

Factor

Works with: Factor version 0.99 development release 2019-03-17
```USING: accessors arrays calendar colors combinators
combinators.short-circuit fonts fry generalizations kernel
literals locals math math.ranges math.vectors namespaces opengl
random sequences timers ui ui.commands ui.gadgets
ui.gadgets.worlds ui.gestures ui.pens.solid ui.render ui.text ;
IN: rosetta-code.galton-box-animation

CONSTANT: pegs \$[ 20 300 40 <range> ]
CONSTANT: speed 90
CONSTANT: balls 140
CONSTANT: peg-color  T{ rgba f 0.60 0.4 0.60 1.0 }
CONSTANT: ball-color T{ rgba f 0.80 1.0 0.20 1.0 }
CONSTANT: slot-color T{ rgba f 0.00 0.2 0.40 1.0 }
CONSTANT: bg-color   T{ rgba f 0.02 0.0 0.02 1.0 }

CONSTANT: font \$[
monospace-font
t >>bold?
T{ rgba f 0.80 1.0 0.20 1.0 } >>foreground
T{ rgba f 0.02 0.0 0.02 1.0 } >>background
]

TUPLE: galton < gadget balls { frame initial: 1 } ;

DEFER: on-tick

galton new bg-color <solid> >>interior V{ } clone >>balls
dup [ on-tick ] curry f speed milliseconds <timer>
start-timer ;

dup frame>> balls <
[ { 250 -20 } swap balls>> [ push ] keep ] when drop ;

: draw-msg ( -- )
{ 10 10 }
[ font "Press <space> for new animation" draw-text ]
with-translation ;

: draw-slots ( -- )
slot-color gl-color { 70 350 } { 70 871 }
10 [ 2dup gl-line [ { 40 0 } v+ ] bi@ ] times 2drop
{ 70 871 } { 430 871 } gl-line ;

: diamond-side ( loc1 loc2 loc3 -- )
[ v+ dup ] [ v+ gl-line ] bi* ;

: draw-diamond ( loc color -- )
gl-color {
[ { 0 -10 } { 10 10 } ]
[ { 10 0 } { -10 10 } ]
[ { 0 10 } { -10 -10 } ]
[ { -10 0 } { 10 -10 } ]
} [ diamond-side ] map-compose cleave ;

: draw-peg-row ( loc n -- )
<iota> [ 40 * 0 2array v+ peg-color draw-diamond ] with
each ;

: draw-peg-triangle ( -- )
{ 250 40 } 1
8 [ 2dup draw-peg-row [ { -20 40 } v+ ] dip 1 + ] times
2drop ;

: draw-balls ( gadget -- )
balls>> [ ball-color draw-diamond ] each ;

: rand-side ( loc -- loc' ) { { 20 20 } { -20 20 } } random v+ ;

:: collide? ( GADGET BALL -- ? )
BALL second :> y
BALL { 0 20 } v+ :> tentative
{ [ y 860 = ] [ tentative GADGET balls>> member? ] } 0|| ;

:: update-ball ( GADGET BALL -- BALL' )
{
{ [ BALL second pegs member? ] [ BALL rand-side ] }
{ [ GADGET BALL collide? ] [ BALL ] }
[ BALL { 0 20 } v+ ]
} cond ;

: update-balls ( gadget -- )
dup '[ [ _ swap update-ball ] map ] change-balls drop ;

: on-tick ( gadget -- )
{
[ dup frame>> odd? [ add-ball ] [ drop ] if ]
[ relayout-1 ] [ update-balls ]
[ [ 1 + ] change-frame drop ]
} cleave ;

M: galton pref-dim* drop { 500 900 } ;

draw-peg-triangle draw-msg draw-slots draw-balls ;

: com-new ( gadget -- ) V{ } clone >>balls 1 >>frame drop ;

galton "gestures" f {
{ T{ key-down { sym " " } } com-new }
} define-command-map

MAIN-WINDOW: galton-box-animation
{
{ title "Galton Box Animation" }
{ window-controls
{ normal-title-bar close-button minimize-button } }
```
Output:

Image taken from the program mid-animation: [1]

Go

Translation of: D
```package main

import (
"fmt"
"math/rand"
"time"
)

const boxW = 41      // Galton box width
const boxH = 37      // Galton box height.
const pinsBaseW = 19 // Pins triangle base.
const nMaxBalls = 55 // Number of balls.

const centerH = pinsBaseW + (boxW-pinsBaseW*2+1)/2 - 1

const (
empty  = ' '
ball   = 'o'
wall   = '|'
corner = '+'
floor  = '-'
pin    = '.'
)

type Ball struct{ x, y int }

func newBall(x, y int) *Ball {
if box[y][x] != empty {
panic("Tried to create a new ball in a non-empty cell. Program terminated.")
}
b := Ball{x, y}
box[y][x] = ball
return &b
}

func (b *Ball) doStep() {
if b.y <= 0 {
return // Reached the bottom of the box.
}
cell := box[b.y-1][b.x]
switch cell {
case empty:
box[b.y][b.x] = empty
b.y--
box[b.y][b.x] = ball
case pin:
box[b.y][b.x] = empty
b.y--
if box[b.y][b.x-1] == empty && box[b.y][b.x+1] == empty {
b.x += rand.Intn(2)*2 - 1
box[b.y][b.x] = ball
return
} else if box[b.y][b.x-1] == empty {
b.x++
} else {
b.x--
}
box[b.y][b.x] = ball
default:
// It's frozen - it always piles on other balls.
}
}

type Cell = byte

/* Galton box. Will be printed upside down. */
var box [boxH][boxW]Cell

func initializeBox() {
// Set ceiling and floor
box[0][0] = corner
box[0][boxW-1] = corner
for i := 1; i < boxW-1; i++ {
box[0][i] = floor
}
for i := 0; i < boxW; i++ {
box[boxH-1][i] = box[0][i]
}

// Set walls
for r := 1; r < boxH-1; r++ {
box[r][0] = wall
box[r][boxW-1] = wall
}

// Set rest to empty initially
for i := 1; i < boxH-1; i++ {
for j := 1; j < boxW-1; j++ {
box[i][j] = empty
}
}

// Set pins
for nPins := 1; nPins <= pinsBaseW; nPins++ {
for p := 0; p < nPins; p++ {
box[boxH-2-nPins][centerH+1-nPins+p*2] = pin
}
}
}

func drawBox() {
for r := boxH - 1; r >= 0; r-- {
for c := 0; c < boxW; c++ {
fmt.Printf("%c", box[r][c])
}
fmt.Println()
}
}

func main() {
rand.Seed(time.Now().UnixNano())
initializeBox()
var balls []*Ball
for i := 0; i < nMaxBalls+boxH; i++ {
fmt.Println("\nStep", i, ":")
if i < nMaxBalls {
balls = append(balls, newBall(centerH, boxH-2)) // add ball
}
drawBox()

// Next step for the simulation.
// Frozen balls are kept in balls slice for simplicity
for _, b := range balls {
b.doStep()
}
}
}
```
Output:

Sample output (showing last step only):

```Step 91 :
+---------------------------------------+
|                                       |
|                   .                   |
|                  . .                  |
|                 . . .                 |
|                . . . .                |
|               . . . . .               |
|              . . . . . .              |
|             . . . . . . .             |
|            . . . . . . . .            |
|           . . . . . . . . .           |
|          . . . . . . . . . .          |
|         . . . . . . . . . . .         |
|        . . . . . . . . . . . .        |
|       . . . . . . . . . . . . .       |
|      . . . . . . . . . . . . . .      |
|     . . . . . . . . . . . . . . .     |
|    . . . . . . . . . . . . . . . .    |
|   . . . . . . . . . . . . . . . . .   |
|  . . . . . . . . . . . . . . . . . .  |
| . . . . . . . . . . . . . . . . . . . |
|                                       |
|                                       |
|                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            |
+---------------------------------------+
```

```import Data.Map hiding (map, filter)
import Graphics.Gloss

data Ball = Ball { position :: (Int, Int), turns :: [Int] }

type World = ( Int           -- number of rows of pins
, [Ball]        -- sequence of balls
, Map Int Int ) -- counting bins

updateWorld :: World -> World
updateWorld (nRows, balls, bins)
| y < -nRows-5  = (nRows, map update bs, bins <+> x)
| otherwise     = (nRows, map update balls, bins)
where
(Ball (x,y) _) : bs = balls

b <+> x = unionWith (+) b (singleton x 1)

update (Ball (x,y) turns)
| -nRows <= y && y < 0 = Ball (x + head turns, y - 1) (tail turns)
| otherwise            = Ball (x, y - 1) turns

drawWorld :: World -> Picture
drawWorld (nRows, balls, bins) = pictures [ color red ballsP
, color black binsP
, color blue pinsP ]
where ballsP = foldMap (disk 1) \$ takeWhile ((3 >).snd) \$ map position balls
binsP  = foldMapWithKey drawBin bins
pinsP  = foldMap (disk 0.2) \$ [1..nRows] >>= \i ->
[1..i] >>= \j -> [(2*j-i-1, -i-1)]

disk r pos = trans pos \$ circleSolid (r*10)
drawBin x h = trans (x,-nRows-7)
\$ rectangleUpperSolid 20 (-fromIntegral h)
trans (x,y) = Translate (20 * fromIntegral x) (20 * fromIntegral y)

startSimulation :: Int -> [Ball] -> IO ()
startSimulation nRows balls = simulate display white 50 world drawWorld update
where display = InWindow "Galton box" (400, 400) (0, 0)
world = (nRows, balls, empty)
update _ _ = updateWorld

main = evalRandIO balls >>= startSimulation 10
where balls = mapM makeBall [1..]
makeBall y = Ball (0, y) <\$> randomTurns
randomTurns = filter (/=0) <\$> getRandomRs (-1, 1)
```

Icon and Unicon

The code here is adapted from the Unicon Book.

```link graphics

global pegsize, pegsize2, height, width, delay

procedure main(args)    # galton box simulation from Unicon book
pegsize2 := (pegsize := 10) * 2    # pegs & steps
delay := 2                         # ms delay
setup_galtonwindow(pegsize)
n := integer(args[1]) | 100        # balls to drop
every 1 to n do galton(pegsize)
WDone()
end

procedure setup_galtonwindow(n)  # Draw n levels of pegs,
local xpos, ypos, i, j
# Pegboard size is 2n-1 square
# Expected max value of histogram is (n, n/2)/2^n
# ... approximate with something simpler?

height := n*n/2*pegsize + (width := (2*n+1)*pegsize)
Window("size=" || width || "," || height, "fg=grayish-white")
WAttrib("fg=dark-grey")
every ypos := (i := 1 to n) * pegsize2 do {
xpos := width/2 - (i - 1) * pegsize - pegsize/2 - pegsize2
every 1 to i do
FillArc(xpos +:= pegsize2, ypos, pegsize, pegsize)
}
WAttrib("fg=black","drawop=reverse")      # set drawing mode for balls
end

procedure galton(n)                          # drop a ball into the galton box
local xpos, ypos, oldx, oldy
xpos := oldx := width/2 - pegsize/2
ypos := oldy := pegsize
every 1 to n do {                         # For every ball...
xpos +:= ((?2 = 1) | -1) * pegsize     # +/- pegsize
animate(.oldx, .oldy, oldx := xpos, oldy := ypos +:= pegsize2)
}
animate(xpos, ypos, xpos, ypos + 40)      # Now the ball falls ...
animate(xpos, ypos+40, xpos, ypos + 200)  # ... to the floor
draw_ball(xpos)                           # Record this ball
end

procedure animate(xfrom, yfrom, xto, yto)
animate_actual(xfrom, yfrom, xto, yfrom, 4)
animate_actual(xto, yfrom, xto, yto, 10)
end

procedure animate_actual(xfrom, yfrom, xto, yto, steps) # attribs already set
local x, y, xstep, ystep, lastx, lasty
x -:= xstep := (xto - (x := xfrom))/steps
y -:= ystep := (yto - (y := yfrom))/steps
every 1 to steps do {
FillArc(lastx := x +:= xstep, lasty := y +:= ystep, pegsize, pegsize)
WDelay(delay)      # wait in ms
FillArc(x, y, pegsize, pegsize)
}
end

procedure draw_ball(x)
static ballcounts
initial ballcounts := table(0)
FillArc(x, height-(ballcounts[x] +:= 1)*pegsize, pegsize, pegsize)
end
```

J

First, we need to represent our pins:

```initpins=: '* ' {~ '1'&i.@(-@|. |."_1 [: ":@-.&0"1 <:~/~)@i.
```

For example:

```   initpins 4
*
* *
* * *
* * * *
```

Note that we could introduce other pin arrangements, for example a Sierpinski triangle:

```initSpins=: [: }.@|. (1- 2&^@>:) ]\ [: ,] (,~ ,.~)@]^:[ ,: bind '* '
```

... but this will not be too interesting to use, because of the lack of interior pins for the balls to bounce off of.

Anyways, once we have that, we can add balls to our picture:

```init=: ' ',. ' ',.~ ] ,~ ' ',~ ' o' {~  (# ' ' ~: 1&{.)
```

For example:

```   3 (init initpins) 4
o
o
o

*
* *
* * *
* * * *
```

Now we just need some way of updating our datastructure.

We will need a mechanism to shift a ball left or right if it's above a pin:

```bounce=: (C.~ ] <"1@:+ 0 1 -~/~ ? @: (2"0))"1 [: I. 'o*'&E."1&.|:
```

And, a mechanism to make the balls fall:

```shift=: 4 :0
fill=. {.0#,y
x |.!.fill y
)
```

And then we need to separate out the balls from the pins, so the balls fall and the pins do not. Note also that in this representation, balls will have to fall when they bounce because they cannot occupy the same space that a pin occupies.

We will also want some way of preventing the balls from falling forever. For this task it's probably sufficient to introduce a baseline just deep enough to hold the stacks (which have passed through the pins) and have later balls instantly fall as close as they can to the baseline once they are passed the pins.

```pins=: '*'&=
balls=: 'o'&=

bounce=: (C.~ 0 1 <@(-/~) [: (+ ?@2:"0) I.)"1

nxt=: ' ',~ [: clean ' *o' {~ pins + 2 * _1 shift balls bounce balls *. 1 shift pins

clean2=: ({. , -.&' '"1&.|:&.|.@}.)~ 1 + >./@(# | '*' i:~"1 |:)
clean1=: #~ 1 1 -.@E. *./"1@:=&' '
clean=: clean1@clean2
```

For example:

```   nxt nxt 3 (init initpins) 4

o
o
o*
* *
* * *
* * * *
```

Or, showing an entire animation sequence:

```   nxt&.>^:a: <7 (init ' ',.' ',.~ initpins) 5
┌─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┐
│      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 │
│    * * *    │    * * *    │   * * * *   │  * * * * *  │             │             │             │             │             │             │             │             │             │             │
│   * * * *   │   * * * *   │  * * * * *  │             │             │             │             │             │             │             │             │             │             │             │
│  * * * * *  │  * * * * *  │             │             │             │             │             │             │             │             │             │             │             │             │
│             │             │             │             │             │             │             │             │             │             │             │             │             │             │
└─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘```

Java

The balls keep track of where they are, and we just have to move them down and print. You might easily adjust this to take command line input for the numbers of pins and balls. I'm sure that this could be a lot shorter...

```import java.util.Random;
import java.util.List;
import java.util.ArrayList;

public class GaltonBox {
public static void main( final String[] args ) {
new GaltonBox( 8, 200 ).run();
}

private final int        m_pinRows;
private final int        m_startRow;
private final Position[] m_balls;
private final Random     m_random = new Random();

public GaltonBox( final int pinRows, final int ballCount ) {
m_pinRows  = pinRows;
m_startRow = pinRows + 1;
m_balls    = new Position[ ballCount ];

for ( int ball = 0; ball < ballCount; ball++ )
m_balls[ ball ] = new Position( m_startRow, 0, 'o' );
}

private static class Position {
int  m_row;
int  m_col;
char m_char;

Position( final int row, final int col, final char ch ) {
m_row  = row;
m_col  = col;
m_char = ch;
}
}

public void run() {
for ( int ballsInPlay = m_balls.length; ballsInPlay > 0;  ) {
ballsInPlay = dropBalls();
print();
}
}

private int dropBalls() {
int ballsInPlay = 0;
int ballToStart = -1;

// Pick a ball to start dropping
for ( int ball = 0; ball < m_balls.length; ball++ )
if ( m_balls[ ball ].m_row == m_startRow )
ballToStart = ball;

// Drop balls that are already in play
for ( int ball = 0; ball < m_balls.length; ball++ )
if ( ball == ballToStart ) {
m_balls[ ball ].m_row = m_pinRows;
ballsInPlay++;
}
else if ( m_balls[ ball ].m_row > 0 && m_balls[ ball ].m_row != m_startRow ) {
m_balls[ ball ].m_row -= 1;
m_balls[ ball ].m_col += m_random.nextInt( 2 );
if ( 0 != m_balls[ ball ].m_row )
ballsInPlay++;
}

return ballsInPlay;
}

private void print() {
for ( int row = m_startRow; row --> 1;  ) {
for ( int ball = 0; ball < m_balls.length; ball++ )
if ( m_balls[ ball ].m_row == row )
printBall( m_balls[ ball ] );
System.out.println();
printPins( row );
}
printCollectors();
System.out.println();
}

private static void printBall( final Position pos ) {
for ( int col = pos.m_row + 1; col --> 0;  )
System.out.print( ' ' );
for ( int col = 0; col < pos.m_col; col++ )
System.out.print( "  " );
System.out.print( pos.m_char );
}

private void printPins( final int row ) {
for ( int col = row + 1; col --> 0;  )
System.out.print( ' ' );
for ( int col = m_startRow - row; col --> 0;  )
System.out.print( ". " );
System.out.println();
}

private void printCollectors() {
final List<List<Position>> collectors = new ArrayList<List<Position>>();

for ( int col = 0; col < m_startRow; col++ ) {
final List<Position> collector = new ArrayList<Position>();

for ( int ball = 0; ball < m_balls.length; ball++ )
if ( m_balls[ ball ].m_row == 0 && m_balls[ ball ].m_col == col )
}

for ( int row = 0, rows = longest( collectors ); row < rows; row++ ) {
for ( int col = 0; col < m_startRow; col++ ) {
final List<Position> collector = collectors.get( col );
final int            pos       = row + collector.size() - rows;

System.out.print( '|' );
if ( pos >= 0 )
System.out.print( collector.get( pos ).m_char );
else
System.out.print( ' ' );
}
System.out.println( '|' );
}
}

private static final int longest( final List<List<Position>> collectors ) {
int result = 0;

for ( final List<Position> collector : collectors )
result = Math.max( collector.size(), result );

return result;
}
}
```
Output:

When only five balls have begun to fall through the pins:

```         o
.
o
. .
o
. . .
o
. . . .
o
. . . . .

. . . . . .

. . . . . . .

. . . . . . . . ```

Later, some balls have arrived in the collectors:

```         o
.
o
. .
o
. . .
o
. . . .
o
. . . . .
o
. . . . . .
o
. . . . . . .
o
. . . . . . . .
| | | | | |o| | | |
| | | |o|o|o| | | |```

Note that the collectors are as deep as required.

Finally, all the balls are in the collectors:

```         .

. .

. . .

. . . .

. . . . .

. . . . . .

. . . . . . .

. . . . . . . .
| | | | |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|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| |```

JavaScript

Works with NodeJs

```const readline = require('readline');

/**
* Galton Box animation
* @param {number} layers The number of layers in the board
* @param {number} balls The number of balls to pass through
*/
const galtonBox = (layers, balls) => {
const speed = 100;
const ball = 'o';
const peg = '.';
const result = [];

const sleep = ms => new Promise(resolve => {
setTimeout(resolve,ms)
});

/**
* The board is represented as a 2D array.
* @type {Array<Array<string>>}
*/
const board = [...Array(layers)]
.map((e, i) => {
const sides = Array(layers - i).fill(' ');
const a = Array(i + 1).fill(peg).join(' ').split('');
return [...sides, ...a, ...sides];
});

/**
* @return {Array<string>}
*/
const emptyRow = () => Array(board[0].length).fill(' ');

/**
* @param {number} i
* @returns {number}
*/
const bounce = i => Math.round(Math.random()) ? i - 1 : i + 1;

/**
* Prints the current state of the board and the collector
*/
const show = () => {
board.forEach(e => console.log(e.join('')));
result.reverse();
result.forEach(e => console.log(e.join('')));
result.reverse();
};

/**
* Collect the result.
* @param {number} idx
*/
const appendToResult = idx => {
const row = result.find(e => e[idx] === ' ');
if (row) {
row[idx] = ball;
} else {
const newRow = emptyRow();
newRow[idx] = ball;
result.push(newRow);
}
};

/**
* Move the balls through the board
* @returns {boolean} True if the there are balls in the board.
*/
const iter = () => {
let hasNext = false;
[...Array(bordSize)].forEach((e, i) => {
const rowIdx = (bordSize - 1) - i;
const idx = board[rowIdx].indexOf(ball);
if (idx > -1) {
board[rowIdx][idx] = ' ';
const nextRowIdx = rowIdx + 1;
if (nextRowIdx < bordSize) {
hasNext = true;
const nextRow = board[nextRowIdx];
nextRow[bounce(idx)] = ball;
} else {
appendToResult(idx);
}
}
});
return hasNext;
};

/**
* Add a ball to the board.
* @returns {number} The number of balls left to add.
*/
const addBall = () => {
board[0][apex] = ball;
balls = balls - 1;
return balls;
};

board.unshift(emptyRow());
result.unshift(emptyRow());

const bordSize = board.length;
const apex = board[1].indexOf(peg);

/**
* Run the animation
*/
(async () => {
await sleep(speed).then(show);
iter();
}
await sleep(speed).then(show);
while (iter()) {
await sleep(speed).then(show);
}
await sleep(speed).then(show);
})();

};

galtonBox(12, 50);
```
Output:
```
.
. .
. . .
. . . .
. . . . .
. . . . . .
. . . . . . .
. . . . . . . .
. . . . . . . . .
. . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . . .
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   ```

Julia

This is a proof of concept code. It does not use external packages. The ASCII animation is running in the stdout terminal, which has to be at least 28 character wide, and 40 character high, and accept ANSI control sequences for positioning the cursor, and clearing the screen (e.g. the Windows console, or ConEmu).

6 pins in 6 rows are hard coded. The next ball is released at the press of the Enter key. Keep it depressed for continuous running. The balls are randomly deflected left or right at hitting the pins, and they fall to the bins at the bottom, which extend downwards. The timer function sets the speed of the animation. Change the "interval" parameter to larger values for slower movement. Pressing x then Enter exits, other keys are ignored.

Works with: Julia version 1.0
```using Random
function drawball(timer)
global r, c, d
print("\e[\$r;\$(c)H ")       # clear last ball position (r,c)
if (r+=1) > 14
close(timer)
b = (bin[(c+2)>>2] += 1)# update count in bin
print("\e[\$b;\$(c)Ho")   # lengthen bar of balls in bin
else
r in 3:2:13 && c in 17-r:4:11+r && (d = 2bitrand()-1)
print("\e[\$r;\$(c+=d)Ho")# show ball moving in direction d
end
end

print("\e[2J")                  # clear screen
for r = 3:2:13, c = 17-r:4:11+r # 6 pins in 6 rows
print("\e[\$r;\$(c)H^")       # draw pins
end
print("\e[15;2H-------------------------")

bin = fill(15,7)                # positions of top of bins
while "x" != readline() >= ""   # x-Enter: exit, {keys..}Enter: next ball
global r,c,d = 0,14,0
t = Timer(drawball, 0, interval=0.1)
while r < 15 sleep(0.01) end
print("\e[40;1H")           # move cursor far down
end
```
Output:
```             ^

^   ^

^   ^   ^

^   ^   ^   ^

^   ^   ^   ^   ^

^   ^   ^   ^   ^   ^

--------------------------
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```

Kotlin

Translation of: D
```// version 1.2.10

import java.util.Random

val boxW = 41       // Galton box width.
val boxH = 37       // Galton box height.
val pinsBaseW = 19  // Pins triangle base.
val nMaxBalls = 55  // Number of balls.

val centerH = pinsBaseW + (boxW - pinsBaseW * 2 + 1) / 2 - 1
val rand = Random()

enum class Cell(val c: Char) {
EMPTY(' '),
BALL('o'),
WALL('|'),
CORNER('+'),
FLOOR('-'),
PIN('.')
}

/* Galton box. Will be printed upside down. */
val box = List(boxH) { Array<Cell>(boxW) { Cell.EMPTY } }

class Ball(var x: Int, var y: Int) {

init {
require(box[y][x] == Cell.EMPTY)
box[y][x] = Cell.BALL
}

fun doStep() {
if (y <= 0) return  // Reached the bottom of the box.
val cell = box[y - 1][x]
when (cell) {
Cell.EMPTY -> {
box[y][x] = Cell.EMPTY
y--
box[y][x] = Cell.BALL
}

Cell.PIN -> {
box[y][x] = Cell.EMPTY
y--
if (box[y][x - 1] == Cell.EMPTY && box[y][x + 1] == Cell.EMPTY) {
x += rand.nextInt(2) * 2 - 1
box[y][x] = Cell.BALL
return
}
else if (box[y][x - 1] == Cell.EMPTY) x++
else x--
box[y][x] = Cell.BALL
}

else -> {
// It's frozen - it always piles on other balls.
}
}
}
}

fun initializeBox() {
// Set ceiling and floor:
box[0][0] = Cell.CORNER
box[0][boxW - 1] = Cell.CORNER
for (i in 1 until boxW - 1) box[0][i] = Cell.FLOOR
for (i in 0 until boxW) box[boxH - 1][i] = box[0][i]

// Set walls:
for (r in 1 until boxH - 1) {
box[r][0] = Cell.WALL
box[r][boxW - 1] = Cell.WALL
}

// Set pins:
for (nPins in 1..pinsBaseW) {
for (pin in 0 until nPins) {
box[boxH - 2 - nPins][centerH + 1 - nPins + pin * 2] = Cell.PIN
}
}
}

fun drawBox() {
for (row in box.reversed()) {
for (i in row.indices) print(row[i].c)
println()
}
}

fun main(args: Array<String>) {
initializeBox()
val balls = mutableListOf<Ball>()
for (i in 0 until nMaxBalls + boxH) {
println("\nStep \$i:")
drawBox()

// Next step for the simulation.
// Frozen balls are kept in balls list for simplicity
for (b in balls) b.doStep()
}
}
```

Sample output (showing final step only):

```Step 91:
+---------------------------------------+
|                                       |
|                   .                   |
|                  . .                  |
|                 . . .                 |
|                . . . .                |
|               . . . . .               |
|              . . . . . .              |
|             . . . . . . .             |
|            . . . . . . . .            |
|           . . . . . . . . .           |
|          . . . . . . . . . .          |
|         . . . . . . . . . . .         |
|        . . . . . . . . . . . .        |
|       . . . . . . . . . . . . .       |
|      . . . . . . . . . . . . . .      |
|     . . . . . . . . . . . . . . .     |
|    . . . . . . . . . . . . . . . .    |
|   . . . . . . . . . . . . . . . . .   |
|  . . . . . . . . . . . . . . . . . .  |
| . . . . . . . . . . . . . . . . . . . |
|                                       |
|                                       |
|                  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        |
+---------------------------------------+
```

Liberty BASIC

User can choose the number of balls to run through the simulation.

```[setup]
nomainwin

speed=50

prompt "Number of balls to drop: ";cycleMax
cycleMax=abs(int(cycleMax))

'create window
WindowWidth=400
WindowHeight=470
UpperLeftX=1
UpperLeftY=1
graphicbox #1.gb, 10, 410,370,25
open "Galton Machine" for graphics_nf_nsb as #1
#1 "trapclose [q];down;fill black;flush"
#1.gb "font courier_new 12"

'Create graphical sprites
#1 "getbmp bg 1 1 400 600"
#1 "place 0 0; color white;backcolor white;boxfilled 17 17;place 8 8;color black;backcolor black;circlefilled 8;"
#1 "place 8 25;color white;backcolor white;circlefilled 8;"
#1 "getbmp ball 0 0 17 34"
#1 "place 8 25;color red;backcolor red;circlefilled 8;"
#1 "getbmp pin 0 0 17 34"
#1 "background bg"

for pinCount = 1 to 28
next pinCount

for ballCount = 1 to 7
next ballCount

'place pins on page
for y = 1 to 7
for x = 1 to y
pin=pin+1
xp=200-x*50+y*25
yp=y*35+100
#1 "spritexy pin";pin;" ";xp;" ";yp
#1 "drawsprites"
next x
next y

'set balls in motion
for a = 1 to 7
#1 "spritexy ball";a;" 174 ";a*60-350
#1 "spritemovexy ball";a;" 0 5"
next a

[start] 'update every 50ms - lower number means faster updates
timer speed, [move]
wait

[move] 'cycle through the sprites to check for contact with pins or dropping off board
#1 "drawsprites"
for ballNum = 1 to 7
gosub [checkCollide]
next ballNum
timer speed, [move]
wait

[checkCollide] 'check for contact with pins or dropping off board
timer 0
#1 "spritexy? ball";ballNum;" x y" 'get current ball position
#1 "spritecollides ball";ballNum;" hits\$" 'collect any collisions
if hits\$<>"" then 'any collisions? if so...
direction = rnd(1)
'randomly bounce either left or right
if direction >0.4999999 then #1 "spritexy ball";ballNum;" ";x+25;" ";y else #1 "spritexy ball";ballNum;" ";x-25;" ";y
#1 "spritemovexy ball";ballNum;" 0 5"'set ball in motion again
end if
#1 "spritexy? ball";ballNum;" x y" 'get current ball position
if y > 400 then 'if ball has dropped off board, then...
select case 'figure out which slot it has landed in and increment the counter for that slot
case x<49
slot(1)=slot(1)+1
case x=49
slot(2)=slot(2)+1
case x=99
slot(3)=slot(3)+1
case x=149
slot(4)=slot(4)+1
case x=199
slot(5)=slot(5)+1
case x=249
slot(6)=slot(6)+1
case x=299
slot(7)=slot(7)+1
case x>299
slot(8)=slot(8)+1
end select
for a = 1 to 8 'write the slot counts in the small graphic box
update\$="place "+str\$((a-1)*48+1)+" 20;\"+str\$(slot(a))
#1.gb, update\$
next a
#1 "spritexy ball";ballNum;" 174 ";0-10 'reposition the sprite just off the top of the screen
#1 "spritemovexy ball";ballNum;" 0 5" 'set the ball in motion again
cycles = cycles + 1 'increment the fallen ball count
if cycles >= cycleMax then
timer 0 'stop animation
'make the visible balls go away
for a = 1 to 7
#1 "spritexy ball";a;" 174 700"
#1 "spritemovexy ball";a;" 0 0"
next a
#1 "drawsprites"
notice "Complete"
wait
end if
end if
return

[q]
close #1
'It is IMPORTANT to unload the bitmaps and clear memory
end```

Lua

Uses Bitmap class here, with an ASCII pixel representation, then extending..

```Bitmap.render = function(self)
for y = 1, self.height do
print(table.concat(self.pixels[y], " "))
end
end

-- globals (tweak here as desired)
math.randomseed(os.time())
local W, H, MIDX = 15, 40, 7
local bitmap = Bitmap(W, H)
local AIR, PIN, BALL, FLOOR = ".", "▲", "☻", "■"
local nballs, balls = 60, {}
local frame, showEveryFrame = 1, false

-- the game board:
bitmap:clear(AIR)
for row = 1, 7 do
for col = 0, row-1 do
bitmap:set(MIDX-row+col*2+1, 1+row*2, PIN)
end
end
for col = 0, W-1 do
bitmap:set(col, H-1, FLOOR)
end

-- ball class
Ball = {
new = function(self, x, y, bitmap)
local instance = setmetatable({ x=x, y=y, bitmap=bitmap, alive=true }, self)
return instance
end,
update = function(self)
if not self.alive then return end
self.bitmap:set(self.x, self.y, AIR)
local newx, newy = self.x, self.y+1
local below = self.bitmap:get(newx, newy)
if below==PIN then
newx = newx + (math.random(2)-1)*2-1
end
local there = self.bitmap:get(newx, newy)
if there==AIR then
self.x, self.y = newx, newy
else
self.alive = false
end
self.bitmap:set(self.x, self.y, BALL)
end,
}
Ball.__index = Ball
setmetatable(Ball, { __call = function (t, ...) return t:new(...) end })

-- simulation:
local function spawn()
if nballs > 0 then
balls[#balls+1] = Ball(MIDX, 0, bitmap)
nballs = nballs - 1
end
end

spawn()
while #balls > 0 do
if frame%2==0 then spawn() end
alive = {}
for _,ball in ipairs(balls) do
ball:update()
if ball.alive then alive[#alive+1]=ball end
end
balls = alive
if frame%50==0 or #alive==0 or showEveryFrame then
print("FRAME "..frame..":")
bitmap:render()
end
frame = frame + 1
end
```
Output:
```FRAME 50:
. . . . . . . . . . . . . . .
. . . . . . . ☻ . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ ▲ . . . . . . .
. . . . . . . . . . . . . . .
. . . . . ☻ ▲ . ▲ . . . . . .
. . . . . . . . . . . . . . .
. . . . . ▲ ☻ ▲ . ▲ . . . . .
. . . . . . . . . . . . . . .
. . . . ▲ . ▲ . ▲ ☻ ▲ . . . .
. . . . . . . . . . . . . . .
. . . ▲ . ▲ ☻ ▲ . ▲ . ▲ . . .
. . . . . . . . . . . . . . .
. . ▲ . ▲ . ▲ ☻ ▲ . ▲ . ▲ . .
. . . . . . . . . . . . . . .
. ▲ . ▲ . ▲ . ▲ ☻ ▲ . ▲ . ▲ .
. . . . . . . . . . . . . . .
. . . . ☻ . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . ☻ . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . ☻ . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . . . . . . . . . .
. . . . ☻ . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . ☻ . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . ☻
. . . . . . . . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . ☻ . . . ☻ . . . ☻ . . . .
. . ☻ . . . ☻ . ☻ . ☻ . . . .
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
FRAME 100:
. . . . . . . . . . . . . . .
. . . . . . . ☻ . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ ▲ . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ▲ ☻ ▲ . . . . . .
. . . . . . . . . . . . . . .
. . . . . ▲ ☻ ▲ . ▲ . . . . .
. . . . . . . . . . . . . . .
. . . . ▲ . ▲ . ▲ ☻ ▲ . . . .
. . . . . . . . . . . . . . .
. . . ▲ . ▲ . ▲ ☻ ▲ . ▲ . . .
. . . . . . . . . . . . . . .
. . ▲ . ▲ ☻ ▲ . ▲ . ▲ . ▲ . .
. . . . . . . . . . . . . . .
. ▲ ☻ ▲ . ▲ . ▲ . ▲ . ▲ . ▲ .
. . . . . . . . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . . . . . . . . . .
. . . . ☻ . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . ☻ . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . ☻ . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . ☻ . ☻ . . . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . ☻ . ☻ . . . .
. . . . ☻ . ☻ . ☻ . ☻ . . . .
. . ☻ . ☻ . ☻ . ☻ . ☻ . . . .
. . ☻ . ☻ . ☻ . ☻ . ☻ . . . .
☻ . ☻ . ☻ . ☻ . ☻ . ☻ . . . ☻
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
FRAME 147:
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . ▲ . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . ▲ . ▲ . . . . . .
. . . . . . . . . . . . . . .
. . . . . ▲ . ▲ . ▲ . . . . .
. . . . . . . . . . . . . . .
. . . . ▲ . ▲ . ▲ . ▲ . . . .
. . . . . . . . . . . . . . .
. . . ▲ . ▲ . ▲ . ▲ . ▲ . . .
. . . . . . . . . . . . . . .
. . ▲ . ▲ . ▲ . ▲ . ▲ . ▲ . .
. . . . . . . . . . . . . . .
. ▲ . ▲ . ▲ . ▲ . ▲ . ▲ . ▲ .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . . . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . . . ☻ . ☻ . . . . . .
. . . . ☻ . ☻ . ☻ . . . . . .
. . . . ☻ . ☻ . ☻ . . . . . .
. . . . ☻ . ☻ . ☻ . . . . . .
. . . . ☻ . ☻ . ☻ . ☻ . . . .
. . ☻ . ☻ . ☻ . ☻ . ☻ . . . .
. . ☻ . ☻ . ☻ . ☻ . ☻ . . . .
. . ☻ . ☻ . ☻ . ☻ . ☻ . . . .
. . ☻ . ☻ . ☻ . ☻ . ☻ . . . .
☻ . ☻ . ☻ . ☻ . ☻ . ☻ . ☻ . ☻
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
```

Mathematica / Wolfram Language

```ClearAll[MakePathFunction]
MakePathFunction[{path_, acumpath_}] :=
Module[{f1, f2, f3, pf, n = Length[path]},
f1 = MapThread[{#1/2, #2 + 0.5 < z <= #2 + 1} &, {acumpath,
n - Range[n + 1]}];
f2 = MapThread[{#1/2 + #2 Sqrt[1/4 - (z - #3)^2], #3 <
z <= #3 + 1/2} &, {acumpath // Most, path, n - Range[n]}];
f3 = {{acumpath[[-1]]/2, z <= 0}};
pf = Piecewise[Evaluate[Join[f1, f2, f3]], 0];
pf
]
MakeScene[pfs_List, zfinals_List, n_Integer, t_] :=
Module[{durations, accumduration, if, part, fixed, relt},
durations = n - zfinals;
accumduration = Accumulate[Prepend[durations, 0]];
if = Interpolation[{accumduration, Range[Length[zfinals] + 1]} //
Transpose, InterpolationOrder -> 1];
part = Floor[if[t]];
If[part > 0,
fixed = Table[{pfs[[i]], z} /. z -> zfinals[[i]], {i, part - 1}];
,
fixed = {};
];
relt = t - accumduration[[part]];
relt = n - relt;
Append[fixed, {pfs[[part]] /. z -> relt, relt}]
]
SeedRandom[1234];
n = 6;
m = 150;
r = 0.25; (* fixed *)
dots =
Catenate@Table[{# - i/2 - 1/2, n - i} & /@ Range[i], {i, n}];
g = Graphics[Disk[#, r] & /@ dots, Axes -> True];

paths = RandomChoice[{-1, 1}, {m, n}];
paths = {#, Accumulate[Prepend[#, 0]]} & /@ paths;
xfinals = paths[[All, 2, -1]];
types = DeleteDuplicates[xfinals];
zfinals = ConstantArray[0, Length[paths]];
Do[
pos = Flatten[Position[xfinals, t]];
zfinals[[pos]] += 0.5 Range[Length[pos]];
,
{t, types}
];
max = Max[zfinals] + 1;
zfinals -= max;
pfs = MakePathFunction /@ paths;
Manipulate[
Graphics[{Disk[#, r] & /@ dots, Red,
Disk[#, r] & /@ MakeScene[pfs, zfinals, n, t]},
PlotRange -> {{-n, n}, {Min[zfinals] - 1, n + 2}},
ImageSize -> 150], {t, 0, Total[n - zfinals] - 0.001}]
```

Nim

Translation of: Go
```import random, strutils

const
BoxW = 41         # Galton box width.
BoxH = 37         # Galton box height.
PinsBaseW = 19    # Pins triangle base.
NMaxBalls = 55    # Number of balls.

const CenterH = PinsBaseW + (BoxW - (PinsBaseW * 2 - 1)) div 2 - 1

type

Cell = enum
cEmpty = " "
cBall = "o"
cWall = "|"
cCorner = "+"
cFloor = "-"
cPin = "."

# Galton box. Will be printed upside-down.
Box = array[BoxH, array[BoxW, Cell]]

Ball = ref object
x, y: int

func initBox(): Box =

# Set ceiling and floor.
result[0][0] = cCorner
result[0][^1] = cCorner
for i in 1..(BoxW - 2):
result[0][i] = cFloor
result[^1] = result[0]

# Set walls.
for i in 1..(BoxH - 2):
result[i][0] = cWall
result[i][^1] = cWall

# Set rest to Empty initially.
for i in 1..(BoxH - 2):
for j in 1..(BoxW - 2):
result[i][j] = cEmpty

# Set pins.
for nPins in 1..PinsBaseW:
for p in 0..<nPins:
result[BoxH - 2 - nPins][CenterH + 1 - nPins + p * 2] = cPin

func newBall(box: var Box; x, y: int): Ball =

doAssert box[y][x] == cEmpty, "Tried to create a new ball in a non-empty cell"
result = Ball(x: x, y: y)
box[y][x] = cBall

proc doStep(box: var Box; b: Ball) =

if b.y <= 0:
return    # Reached the bottom of the box.

case box[b.y-1][b.x]

of cEmpty:
box[b.y][b.x] = cEmpty
dec b.y
box[b.y][b.x] = cBall

of cPin:
box[b.y][b.x] = cEmpty
dec b.y
if box[b.y][b.x-1] == cEmpty and box[b.y][b.x+1] == cEmpty:
inc b.x, 2 * rand(1) - 1
elif box[b.y][b.x-1] == cEmpty:
inc b.x
else:
dec b.x
box[b.y][b.x] = cBall

else:
# It's frozen - it always piles on other balls.

proc draw(box: Box) =
for r in countdown(BoxH - 1, 0):
echo box[r].join()

#———————————————————————————————————————————————————————————————————————————————————————————————————

randomize()
var box = initBox()
var balls: seq[Ball]

for i in 0..<(NMaxBalls + BoxH):

echo "Step ", i, ':'
if i < NMaxBalls:
box.draw()

# Next step for the simulation.
# Frozen balls are kept in balls slice for simplicity.
for ball in balls:
box.doStep(ball)
```
Output:

Sample output (showing last step only):

```Step 91:
+---------------------------------------+
|                                       |
|                   .                   |
|                  . .                  |
|                 . . .                 |
|                . . . .                |
|               . . . . .               |
|              . . . . . .              |
|             . . . . . . .             |
|            . . . . . . . .            |
|           . . . . . . . . .           |
|          . . . . . . . . . .          |
|         . . . . . . . . . . .         |
|        . . . . . . . . . . . .        |
|       . . . . . . . . . . . . .       |
|      . . . . . . . . . . . . . .      |
|     . . . . . . . . . . . . . . .     |
|    . . . . . . . . . . . . . . . .    |
|   . . . . . . . . . . . . . . . . .   |
|  . . . . . . . . . . . . . . . . . .  |
| . . . . . . . . . . . . . . . . . . . |
|                                       |
|                                       |
|                                       |
|                      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          |
+---------------------------------------+```

Perl

translated from Raku

Output shows of final state for a run with 50 coins.

Translation of: Raku
```use strict;
use warnings;

use List::Util 'any';
use Time::HiRes qw(sleep);
use List::AllUtils <pairwise pairs>;

use utf8;
binmode STDOUT, ':utf8';

my \$coins      = shift || 100;
my \$peg_lines  = shift || 13;
my \$row_count  = \$peg_lines;
my \$peg        = '^';
my @coin_icons = ("\N{UPPER HALF BLOCK}", "\N{LOWER HALF BLOCK}");

my @coins = (undef) x (3 + \$row_count + 4);
my @stats = (0) x (\$row_count * 2);
\$coins[0] = 0; # initialize with first coin

while (1) {
my \$active = 0;
# if a coin falls through the bottom, count it
\$stats[\$coins[-1] + \$row_count]++ if defined \$coins[-1];

# move every coin down one row
for my \$line (reverse 1..(3+\$row_count+3) ) {
my \$coinpos = \$coins[\$line - 1];

#\$coins[\$line] = do if (! defined \$coinpos) x
if (! defined \$coinpos) {
\$coins[\$line] = undef
} elsif (hits_peg(\$coinpos, \$line)) {
# when a coin from above hits a peg, it will bounce to either side.
\$active = 1;
\$coinpos += rand() < .5 ? -1 : 1;
\$coins[\$line] = \$coinpos
} else {
# if there was a coin above, it will fall to this position.
\$active = 1;
\$coins[\$line] = \$coinpos;
}
}
# let the coin dispenser blink and turn it off if we run out of coins
if (defined \$coins[0]) {
\$coins[0] = undef;
} elsif (--\$coins > 0) {
\$coins[0] = 0
}

for (<0 1>) {
display_board(\@coins, \@stats, \$_);
sleep .1;
}
exit unless \$active;
}

sub display_board {
my(\$p_ref, \$s_ref, \$halfstep) = @_;
my @positions = @\$p_ref;
my @stats     = @\$s_ref;
my \$coin      = \$coin_icons[\$halfstep];

my @board = do {
my @tmpl;

sub out {
my(@stuff) = split '', shift;
my @line;
push @line, ord(\$_) for @stuff;
[@line];
}

push @tmpl, out("  " . " "x(2 * \$row_count)) for 1..3;
my @a = reverse 1..\$row_count;
my @b = 1..\$row_count;
my @pairs = pairwise { (\$a, \$b) } @a, @b;
for ( pairs @pairs ) {
my ( \$spaces, \$pegs ) = @\$_;
push @tmpl, out("  " . " "x\$spaces . join(' ',(\$peg) x \$pegs) . " "x\$spaces);
}
push @tmpl, out("  " . " "x(2 * \$row_count)) for 1..4;
@tmpl;
};

my \$midpos = \$row_count + 2;

our @output;
{
# collect all the output and output it all at once at the end
sub printnl { my(\$foo) = @_; push @output, \$foo . "\n" }
sub printl  { my(\$foo) = @_; push @output, \$foo        }

# make some space above the picture
printnl("") for 0..9;

# place the coins
for my \$line (0..\$#positions) {
my \$pos = \$positions[\$line];
next unless defined \$pos;
\$board[\$line][\$pos + \$midpos] = ord(\$coin);
}
# output the board with its coins
for my \$line (@board) {
printnl join '', map { chr(\$_) } @\$line;
}

# show the statistics
while (any {\$_> 0} @stats) {
printl "  ";
for my \$i (0..\$#stats) {
if (\$stats[\$i] == 1) {
printl "\N{UPPER HALF BLOCK}";
\$stats[\$i]--;
} elsif (\$stats[\$i] <= 0) {
printl " ";
\$stats[\$i] = 0
} else {
printl "\N{FULL BLOCK}";
\$stats[\$i]--; \$stats[\$i]--;
}
}
printnl("");
}
}

print join('', @output) . "\n";
}

sub hits_peg {
my(\$x, \$y) = @_;
3 <= \$y && \$y < (3 + \$row_count) and -(\$y - 2) <= \$x && \$x <= \$y - 2
? not 0 == (\$x - \$y) % 2
: 0
}
```
Output:
```         ^
^ ^
^ ^ ^
^ ^ ^ ^
^ ^ ^ ^ ^
^ ^ ^ ^ ^ ^
^ ^ ^ ^ ^ ^ ^

█ █ █ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ ▀
▀ █ █
█
```

native Perl

Runs until a bottom column overflows.

```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Galton_box_animation
use warnings;
\$| = 1;

my \$width = shift // 7;
my \$bottom = 15;
my \$blank = ' ' x ( 2 * \$width + 1 ) . "\n";
my \$line = ' ' x \$width . '*' . ' ' x \$width . "\n";
local \$_ = join '', \$blank x 5 . \$line,
map({ \$line =~ s/ \* (.*) /* * \$1/; (\$blank, \$line) } 2 .. \$width ),
\$blank x \$bottom;

my \$gap = / \n/ && \$-[0];
my \$gl = qr/.{\$gap}/s;
my \$g = qr/.\$gl/s;
my \$center = \$gap >> 1;
my %path = ('O* ' => 'O*X', ' *O' => 'X*O');

print "\e[H\e[J\$_";
while( not /(?:O\$g){\$bottom}/ )
{
my \$changes = s!O(\$gl)( \* |O\* | \*O)! " \$1" .
(\$path{\$2} // (rand(2) < 1 ? "X* " : " *X")) !ge +
s/O(\$g) / \$1X/g +
s/^ {\$center}\K (\$g \$g) /O\$1 /;
tr/X/O/;
print "\e[H\$_";
\$changes or last;
select undef, undef, undef, 0.05;
}
```
Output:
```

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
```

Phix

console

First, a console version:

```without js -- clear_screen(), text_color(), position(), sleep(), get_key()...
constant balls = 80
clear_screen()
sequence screen = repeat(repeat(' ',23),12)
& repeat(join(repeat(':',12)),12)
& {repeat('.',23)},
Pxy = repeat({12,1},balls)
for peg=1 to 10 do
screen[peg+2][13-peg..11+peg] = join(repeat('.',peg))
end for
puts(1,join(screen,"\n"))
text_color(BRIGHT_RED)
bool moved = true
integer top = ' '   -- (new drop every other iteration)
while moved or top!=' ' do
moved = false
for i=1 to balls do
integer {Px,Py} = Pxy[i]
if Py!=1 or top=' ' then
integer Dx = 0, Dy = 0
if screen[Py+1,Px]=' ' then     -- can vertical?
Dy = 1
else
Dx = {-1,+1}[rand(2)]       -- try l;r or r;l
if screen[Py+1,Px+Dx]!=' ' then Dx = -Dx end if
if screen[Py+1,Px+Dx]==' ' then
Dy = 1
end if
end if
if Dy then
position(Py,Px)  puts(1," ")  screen[Py,Px] = ' '
Px += Dx
Py += Dy
position(Py,Px)  puts(1,"o")  screen[Py,Px] = 'o'
Pxy[i] = {Px,Py}
moved = true
if Py=2 then top = 'o' end if
end if
end if
end for
position(26,1)
sleep(0.2)
if get_key()!=-1 then exit end if
top = screen[2][12]
end while
```
Output:
```           .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: : : :
.......................
```

gui

Also, here is a slightly nicer and resize-able gui version:

Library: Phix/pGUI
Library: Phix/online

You can run this online here.

```--
-- demo\rosetta\GaltonBox.exw
-- ==========================
--
-- Author Pete Lomax, May 2017
--
with javascript_semantics
constant TITLE = "Galton Box"

include pGUI.e

Ihandle dlg, canvas, timershow
cdCanvas cddbuffer, cdcanvas

integer brem = 80
sequence balls = {{0,1,0}}
sequence bins = repeat(0,8)

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, /*posy*/)
integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE"), x, y
atom xx, yy
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
-- draw the pins, then balls, then bins
cdCanvasSetForeground(cddbuffer, CD_DARK_GREEN)
integer pinsize = min(floor(h/40),floor(w/50))
for y=4 to 16 by 2 do
for x=-(y-4) to (y-4) by 4 do
xx = w/2 + x*w/32
yy = h -y*h/32
cdCanvasSector(cddbuffer, xx, yy, pinsize, pinsize, 0, 360)
end for
end for
cdCanvasSetForeground(cddbuffer, CD_INDIGO)
for i=1 to length(balls) do
{x, y} = balls[i]
xx = w/2 + x*w/32
yy = h -y*h/32
cdCanvasSector(cddbuffer, xx, yy, pinsize*4, pinsize*4, 0, 360)
end for
cdCanvasSetLineWidth(cddbuffer,w/9)
for i=1 to length(bins) do
xx = w/2+(i*4-18)*w/32
yy = bins[i]*h/64+10
cdCanvasLine(cddbuffer,xx,10,xx,yy)
end for
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function

function timer_cb(Ihandle ih)
integer x, y=9, dx
if length(balls) then
{x,y,dx} = balls[1]
if y>20 then
integer bindx = (x+18)/4
bins[bindx] += 1
balls = balls[2..\$]
end if
end if
for i=1 to length(balls) do
{x,y,dx} = balls[i]
if y>15 then
dx = 0
elsif and_bits(y,1)=0 then
dx = {-1,+1}[rand(2)]
end if
balls[i] = {x+dx,y+1,dx}
end for
if y>4 and brem!=0 then
brem -= 1
balls = append(balls,{0,1,0})
end if
if brem=0 and length(balls)=0 then
IupSetAttribute(timershow,"RUN","NO")
end if
IupUpdate(canvas)
return IUP_IGNORE
end function

function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_GREY)
return IUP_DEFAULT
end function

procedure main()
IupOpen()

canvas = IupCanvas("RASTERSIZE=360x600")
IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"),
"ACTION", Icallback("redraw_cb")})

timershow = IupTimer(Icallback("timer_cb"), 80)

dlg = IupDialog(canvas, `TITLE="%s"`, {TITLE})

IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
if platform()!=JS then
IupMainLoop()
IupClose()
end if
end procedure

main()
```

PicoLisp

```(de galtonBox (Pins Height)
(let (Bins (need (inc (* 2 Pins)) 0)  X 0  Y 0)
(until (= Height (apply max Bins))
(call 'clear)
(cond
((=0 Y) (setq X (inc Pins)  Y 1))
((> (inc 'Y) Pins)
(inc (nth Bins X))
(zero Y) ) )
((if (rand T) inc dec) 'X)
(for Row Pins
(for Col (+ Pins Row 1)
(let D (dec (- Col (- Pins Row)))
(prin
(cond
((and (= X Col) (= Y Row)) "o")
((and (gt0 D) (bit? 1 D)) ".")
(T " ") ) ) ) )
(prinl) )
(prinl)
(for H (range Height 1)
(for B Bins
(prin (if (>= B H) "o" " ")) )
(prinl) )
(wait 200) ) ) )```

Test:

`(galtonBox 9 11)`
Output:
```# Snapshot after a few seconds:
.
. .
. . .
. . . .
. . . . .
.o. . . . .
. . . . . . .
. . . . . . . .
. . . . . . . . .

o
o o
o o o o```
```# Final state:
.
. .
. . .
. . . .
. . . . .
. . . . . .
. . . . . . .
. . . . . . . .
. . . . . . . . .

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```

Prolog

Works with SWI-Prolog and XPCE.

```:- dynamic tubes/1.
:- dynamic balls/2.
:- dynamic stop/1.

% number of rows of pins (0 -> 9)
row(9).

galton_box :-
retractall(tubes(_)),
retractall(balls(_,_)),
retractall(stop(_)),
assert(stop(@off)),
new(D, window('Galton Box')),
send(D, size, size(520,700)),
display_pins(D),
new(ChTubes, chain),
assert(tubes(ChTubes)),
display_tubes(D, ChTubes),
new(Balls, chain),
new(B, ball(D)),
send(Balls, append, B),
assert(balls(Balls, D)),
send(D, done_message, and(message(ChTubes, clear),
message(ChTubes, free),
message(Balls, for_all, message(@arg1, free)),
message(Balls, clear),
message(Balls, free),
send(D, open).

% class pin, balls travel between pins
:- pce_begin_class(pin, circle, "pin").

initialise(P, Pos) :->
send(P, send_super, initialise, 18),
send(P, fill_pattern, new(_, colour(@default, 0, 0, 0))),
get(Pos, x, X),
get(Pos, y, Y),
send(P, geometry, x := X, y := Y).
:- pce_end_class.

% class tube, balls fall in them
:- pce_begin_class(tube, path, "tube where balls fall").

variable(indice, any, both, "index of the tube in the list").
variable(balls, any, both, "number of balls inside").

initialise(P, Ind, D) :->
row(Row),
send(P, send_super, initialise, kind := poly),
send(P, slot, balls, 0),
send(P, slot, indice, Ind),
X0 is 228 - Row * 20 + Ind * 40,
X1 is X0 + 20,
Y1 is 600, Y0 is 350,
send_list(P, append, [point(X0, Y0), point(X0, Y1),
point(X1,Y1), point(X1,Y0)]),
send(D, display, P).

% animation stop when a tube is full
get(P, slot, balls, B),
B1 is B+1,
send(P, slot, balls, B1),
(   B1 = 12
->  retract(stop(_)), assert(stop(@on))
;   true).
:- pce_end_class.

% class ball
:- pce_begin_class(ball, circle, "ball").

variable(angle, any, both, "angle of the ball with the pin").
variable(dir, any, both, "left / right").
variable(pin, point, both, "pin under the ball when it falls").
variable(position, point, both, "position of the ball").
variable(max_descent, any, both, "max descent").
variable(state, any, both, "in_pins / in_tube").
variable(window, any, both, "window to display").
variable(mytimer, timer, both, "timer of the animation").

initialise(P, W) :->
send(P, send_super, initialise, 18),
send(P, pen, 0),
send(P, state, in_pins),
send(P, fill_pattern, new(_, colour(@default, 65535, 0, 0))),
Ang is 3 * pi / 2,
send(P, slot, angle, Ang),
send(P, slot, window, W),
send(P, geometry, x := 250, y := 30),
send(P, pin, point(250, 50)),
send(P, choose_dir),
send(P, mytimer, new(_, timer(0.005, message(P, move_ball)))),
send(W, display, P),
send(P?mytimer, start).

% method called when the object is destroyed
% first the timer is stopped
% then all the resources are freed
send(P?mytimer, stop),

choose_dir(P) :->
I is random(2),
(   I = 1 -> Dir = left; Dir = right),
send(P, dir, Dir).

move_ball(P) :->
get(P, state, State),
(   State = in_pins
->  send(P, move_ball_in_pins)
;   send(P, move_ball_in_tube)).

move_ball_in_pins(P) :->
get(P, slot, angle, Ang),
get(P, slot, pin, Pin),
get(P, slot, dir, Dir),
(   Dir = left -> Ang1 is Ang-0.15 ; Ang1 is Ang + 0.15),
get(Pin, x, PX),
get(Pin, y, PY),
X is 21 * cos(Ang1) +  PX,
Y is 21 * sin(Ang1) + PY,
send(P, geometry, x := X, y := Y),
send(P?window, display, P),
(   abs(Ang1 - pi) < 0.1
->  PX1 is PX - 20,
send(P, next_move, PX1, PY)
;   abs(Ang1 - 2 * pi) < 0.1
->  PX1 is PX + 20,
send(P, next_move, PX1, PY)
;   send(P, slot, angle, Ang1)).

next_move(P, PX, PY) :->
row(Row),

Ang2 is 3 * pi / 2,
PY1 is PY + 30,
(	PY1 =:= (Row + 1) * 30 + 50
->	send(P, slot, state, in_tube),
NumTube is round((PX - 228 + Row * 20) / 40),
tubes(ChTubes),
get(ChTubes, find,
message(@prolog, same_value,@arg1?indice, NumTube),
Tube),
get(Tube, slot, balls, Balls),
Max_descent is 600 - Balls * 20,
send(P, slot, max_descent, Max_descent),
send(P, slot, position, point(PX, PY))
;	send(P, choose_dir),
send(P, slot, angle, Ang2),
send(P, slot, pin, point(PX, PY1))).

move_ball_in_tube(P) :->
get(P, slot, position, Descente),
get(Descente, x, PX1),
get(Descente, y, PY),
PY1 is PY+4,
send(P, geometry, x := PX1, y := PY1),
get(P, slot, max_descent, Max_descent),
(   Max_descent =< PY1
->  send(P?mytimer, stop),
(	stop(@off) ->  send(@prolog, next_ball); true)
;   send(P, slot, position, point(PX1, PY1))),
send(P?window, display, P).

:- pce_end_class.

next_ball :-
retract(balls(Balls, D)),
new(B, ball(D)),
send(Balls, append, B),
assert(balls(Balls, D)).

% test to find the appropriate tube
same_value(V, V).

display_pins(D) :-
row(Row),
forall(between(0, Row, I),
(  Start is 250 - I * 20,
Y is I * 30 + 50,
forall(between(0, I, J),
(   X is Start + J * 40,
new(P, pin(point(X,Y))),
send(D, display, P))))).

display_tubes(D, Ch) :-
row(Row),
Row1 is Row+1,
forall(between(0, Row1, I),
(   new(T, tube(I, D)),
send(Ch, append, T),
send(D, display, T))).
```

PureBasic

Translation of: Unicon
```Global pegRadius, pegSize, pegSize2, height, width, delay, histogramSize, ball

Procedure eventLoop()
Protected event
Repeat
event = WindowEvent()
If event = #PB_Event_CloseWindow
End
EndIf
Until event = 0
EndProcedure

Procedure animate_actual(x1, y1, x2, y2, steps)
Protected x.f, y.f, xstep.f, ystep.f, i, lastX.f, lastY.f
x = x1
y = y1
xstep = (x2 - x1)/steps
ystep = (y2 - y1)/steps
For i = 1 To steps
lastX = x
lastY = y
StartDrawing(CanvasOutput(0))
DrawingMode(#PB_2DDrawing_XOr)
Circle(x, y, pegRadius, RGB(0, 255, 255))
StopDrawing()
eventLoop()
Delay(delay)      ; wait in ms
StartDrawing(CanvasOutput(0))
DrawingMode(#PB_2DDrawing_XOr)
Circle(x, y, pegRadius, RGB(0, 255, 255))
StopDrawing()
eventLoop()
x + xstep
y + ystep
Next
EndProcedure

Procedure draw_ball(xpos, ypos)
Static Dim ballcounts(0) ;tally drop positions
If xpos > ArraySize(ballcounts())
Redim ballcounts(xpos)
EndIf
ballcounts(xpos) + 1
animate_actual(xpos, ypos, xpos, height - ballcounts(xpos) * pegSize, 20)
StartDrawing(CanvasOutput(0))
Circle(xpos, height - ballcounts(xpos) * pegSize, pegRadius, RGB(255, 0, 0))
StopDrawing()
eventLoop()
If ballcounts(xpos) <= histogramSize
ProcedureReturn 1
EndIf
SetWindowTitle(0, "Ended after " + Str(ball) + " balls") ;histogramSize exceeded
EndProcedure

Procedure animate(x1, y1, x2, y2)
animate_actual(x1, y1, x2, y1, 4)
animate_actual(x2, y1, x2, y2, 10)
EndProcedure

Procedure galton(pegRows)
;drop a ball into the galton box
Protected xpos, ypos, i, oldX, oldY

oldX = width / 2 - pegSize / 2
xpos = oldX
oldY = pegSize
ypos = oldY
animate_actual(oldX, 0, xpos, ypos, 10)
For i = 1 To pegRows
If Random(1)
xpos + pegSize
Else
xpos - pegSize
EndIf
ypos + pegSize2
animate(oldX, oldY, xpos, ypos)
oldX = xpos
oldY = ypos
Next

ProcedureReturn draw_ball(xpos, ypos)
EndProcedure

Procedure setup_window(numRows, ballCount)
;Draw numRows levels of pegs
Protected xpos, ypos, i, j

width = (2 * numRows + 2) * pegSize
histogramSize = (ballCount + 2) / 3
If histogramSize > 500 / pegSize: histogramSize = 500 / pegSize: EndIf
height = width + histogramSize * pegSize
OpenWindow(0, 0, 0, width, height, "Galton box animation", #PB_Window_SystemMenu)

StartDrawing(CanvasOutput(0))
Box(0, 0, width, height, RGB(\$EB, \$EB, \$EB))
For i = 1 To numRows
ypos = i * pegSize2
xpos = width / 2 - (i - 1) * pegSize - pegSize / 2
For j = 1 To i
Circle(xpos, ypos, pegRadius, RGB(0, 0, 255))
xpos + pegSize2
Next
Next
For i = 1 To numRows
Line((numRows - i + 1) * pegSize2 - pegSize / 2, width - pegSize, 1, histogramSize * pegSize, 0)
Next
StopDrawing()
EndProcedure

;based on the galton box simulation from Unicon book
Define pegRows = 10, ballCount
pegSize = pegRadius * 2 + 1
pegSize2 = pegSize * 2
delay = 2                      ; ms delay

Repeat
ballCount = Val(InputRequester("Galton box simulator","How many balls to drop?", "100"))
Until ballCount > 0

setup_window(pegRows, ballCount)
eventLoop()
For ball = 1 To ballCount
If Not galton(pegRows): Break: EndIf
Next
Repeat: eventLoop(): ForEver```

Python

```#!/usr/bin/python

import sys, os
import random
import time

def print_there(x, y, text):
sys.stdout.write("\x1b7\x1b[%d;%df%s\x1b8" % (x, y, text))
sys.stdout.flush()

class Ball():
def __init__(self):
self.x = 0
self.y = 0

def update(self):
self.x += random.randint(0,1)
self.y += 1

def fall(self):
self.y +=1

class Board():
def __init__(self, width, well_depth, N):
self.balls = []
self.fallen = [0] * (width + 1)
self.width = width
self.well_depth = well_depth
self.N = N
self.shift = 4

def update(self):
for ball in self.balls:
if ball.y < self.width:
ball.update()
elif ball.y < self.width + self.well_depth - self.fallen[ball.x]:
ball.fall()
elif ball.y == self.width + self.well_depth - self.fallen[ball.x]:
self.fallen[ball.x] += 1
else:
pass

def balls_on_board(self):
return len(self.balls) - sum(self.fallen)

if(len(self.balls) <= self.N):
self.balls.append(Ball())

def print_board(self):
for y in range(self.width + 1):
for x in range(y):
print_there( y + 1 ,self.width - y + 2*x + self.shift + 1, "#")
def print_ball(self, ball):
if ball.y <= self.width:
x = self.width - ball.y + 2*ball.x + self.shift
else:
x = 2*ball.x + self.shift
y = ball.y + 1
print_there(y, x, "*")

def print_all(self):
print(chr(27) + "[2J")
self.print_board();
for ball in self.balls:
self.print_ball(ball)

def main():
board = Board(width = 15, well_depth = 5, N = 10)
while(board.balls_on_board() > 0):
board.print_all()
time.sleep(0.25)
board.update()
board.print_all()
time.sleep(0.25)
board.update()

if __name__=="__main__":
main()
```

Racket

This does not use the default #lang racket. Required is advanced student with teachpacks universe and image. Multiple balls are added each step, but they do not collide.

```;a ball's position...row is a natural number and col is an integer where 0 is the center
(define-struct pos (row col))
;state of simulation...list of all positions and vector of balls (index = bin)
(define-struct st (poss bins))
;increment vector @i
(define (vector-inc! v i) (vector-set! v i (add1 (vector-ref v i))))

;for balls to fit perfectly between diamond-shaped pins, the side length is
;determined by inscribing the diamond in the circle
(define PIN-SIDE-LENGTH (* (sqrt 2) BALL-RADIUS))
;ultimate pin width and height
(define PIN-HOR-SPACING (* 2 PIN-WH))
;vertical space is the height of an equilateral triangle with side length = PIN-HOR-SPACING
(define PIN-VER-SPACING (* 1/2 (sqrt 3) PIN-HOR-SPACING))
;somewhat copying BASIC256's graphics
;determines how thick the outline will be
(define FILL-RATIO 0.7)
;freeze is a function that converts the drawing code into an actual bitmap forever
(define PIN (freeze (overlay (rotate 45 (square (* FILL-RATIO PIN-SIDE-LENGTH) "solid" "purple"))
(rotate 45 (square PIN-SIDE-LENGTH "solid" "magenta")))))
(define BALL (freeze (overlay (circle (* FILL-RATIO BALL-RADIUS) "solid" "green")
(define BIN-COLOR (make-color 255 128 192))
;# balls bin can fit
(define BIN-CAPACITY 10)
(define BIN-HEIGHT (* BIN-CAPACITY PIN-WH))
(define BIN (freeze (beside/align "bottom"
(line 0 BIN-HEIGHT BIN-COLOR)
(line PIN-WH 0 BIN-COLOR)
(line 0 BIN-HEIGHT BIN-COLOR))))

(define draw-background
(let ([background #f])
(λ (height)
(if (image? background)
background
(let* ([w (+ (image-width BIN) (* PIN-HOR-SPACING height))]
[h (+ PIN-WH (image-height BIN) (* PIN-VER-SPACING height))]
[draw-background (λ () (rectangle w h "solid" "black"))])
(begin (set! background (freeze (draw-background))) background))))))

;draws images using x horizontal space between center points
(define (spaced/x x is)
(if (null? is)
(empty-scene 0 0)
(let spaced/x ([n 1] [i (car is)] [is (cdr is)])
(if (null? is)
i
(overlay/xy i (* -1 n x) 0 (spaced/x (add1 n) (car is) (cdr is)))))))

(define (draw-pin-row r) (spaced/x PIN-HOR-SPACING (make-list (add1 r) PIN)))

;draws all pins, using saved bitmap for efficiency
(define draw-pins
(let ([bmp #f])
(λ (height)
(let ([draw-pins (λ () (foldl (λ (r i) (overlay/align/offset
;vertically line up all pin rows
"center" "bottom" (draw-pin-row r)
;shift down from the bottom of accum'ed image by ver spacing
0 (- PIN-VER-SPACING) i))
(draw-pin-row 0) (range 1 height 1)))])
(if (image? bmp)
bmp
(begin (set! bmp (freeze (draw-pins))) bmp))))))

(define (draw-ball p i)
;the ball starts at the top of the image
(overlay/align/offset "center" "top" BALL (* -1 (pos-col p) PIN-WH) (* -1 (pos-row p) PIN-VER-SPACING) i))

;bin has balls added from bottom, stacked exactly on top of each other
;the conditional logic is needed because above can't handle 0 or 1 things
(define (draw-bin n)
(if (zero? n)
BIN
(overlay/align "center" "bottom"
(if (= n 1) BALL (apply above (make-list n BALL)))
BIN)))

;main drawing function
(define (draw height s)
(let* ([bins (spaced/x PIN-HOR-SPACING (map draw-bin (vector->list (st-bins s))))]
;pins above bins
[w/pins (above (draw-pins height) bins)]
;draw this all one ball diameter (PIN-WH) below top
[w/background (overlay/align/offset "center" "top" w/pins
0 (- PIN-WH) (draw-background height))])
;now accumulate in each ball
(foldl draw-ball w/background (st-poss s))))

;a ball moves down by increasing its row and randomly changing its col by -1 or 1
(define (next-row height p)
(+ -1 (* 2 (random 2)) (pos-col p))))

;each step, every ball goes to the next row and new balls are added at the top center
;balls that fall off go into bins
(define (tock height s)
(let* ([new-ps (map (λ (p) (next-row height p)) (st-poss s))]
;live balls haven't gone past the last row of pins
[live (filter (λ (p) (< (pos-row p) height)) new-ps)]
;dead balls have (partition from normal Racket would be useful here...)
[dead (filter (λ (p) (>= (pos-row p) height)) new-ps)]
;adjust col from [-x,x] to [0,2x]
[bin-indices (map (λ (p) (quotient (+ (pos-col p) height) 2)) dead)])
;add new balls to the live balls
(make-st (append (make-list (random 4) (make-pos 0 0)) live)
;sum dead ball positions into bins
(begin (for-each (λ (i) (vector-inc! (st-bins s) i)) bin-indices)
(st-bins s)))))

;run simulation with empty list of positions to start, stepping with "tock" and drawing with "draw"
(define (run height)
(big-bang (make-st '() (make-vector (add1 height) 0))
(on-tick (λ (ps) (tock height ps)) 0.5)
(to-draw (λ (ps) (draw height ps)))))
```

Raku

(formerly Perl 6)

Works with: rakudo version 2015-09-12
```my \$row-count = 6;

constant \$peg = "*";
constant @coin-icons = "\c[UPPER HALF BLOCK]", "\c[LOWER HALF BLOCK]";

sub display-board(@positions, @stats is copy, \$halfstep) {
my \$coin = @coin-icons[\$halfstep.Int];

state @board-tmpl = {
# precompute a board
my @tmpl;
sub out(*@stuff) {
@tmpl.push: \$[@stuff.join>>.ords.flat];
}
# three lines of space above
for 1..3 {
out "  ", " " x (2 * \$row-count);
}
# \$row-count lines of pegs
for flat (\$row-count...1) Z (1...\$row-count) -> \$spaces, \$pegs {
out "  ", " " x \$spaces, (\$peg xx \$pegs).join(" "), " " x \$spaces;
}
# four lines of space below
for 1..4 {
out "  ", " " x (2 * \$row-count);
}
@tmpl
}();

my \$midpos = \$row-count + 2;

my @output;
{
# collect all the output and output it all at once at the end
sub say(Str \$foo) {
@output.push: \$foo, "\n";
}
sub print(Str \$foo) {
@output.push: \$foo;
}

# make some space above the picture
say "" for ^10;

my @output-lines = map { [ @\$_ ] }, @board-tmpl;
# place the coins
for @positions.kv -> \$line, \$pos {
next unless \$pos.defined;
@output-lines[\$line][\$pos + \$midpos] = \$coin.ord;
}
# output the board with its coins
for @output-lines -> @line {
say @line.chrs;
}

# show the statistics
while any(@stats) > 0 {
print "  ";
@stats = do for @stats -> \$stat {
given \$stat {
when 1 {
print "\c[UPPER HALF BLOCK]";
\$stat - 1;
}
when * <= 0 {
print " ";
0
}
default {
print "\c[FULL BLOCK]";
\$stat - 2;
}
}
}
say "";
}
}
say @output.join("");
}

sub simulate(\$coins is copy) {
my \$alive = True;

sub hits-peg(\$x, \$y) {
if 3 <= \$y < 3 + \$row-count and -(\$y - 2) <= \$x <= \$y - 2 {
return not (\$x - \$y) %% 2;
}
return False;
}

my @coins = Int xx (3 + \$row-count + 4);
my @stats = 0 xx (\$row-count * 2);
# this line will dispense coins until turned off.
@coins[0] = 0;
while \$alive {
\$alive = False;
# if a coin falls through the bottom, count it
given @coins[*-1] {
when *.defined {
@stats[\$_ + \$row-count]++;
}
}

# move every coin down one row
for ( 3 + \$row-count + 3 )...1 -> \$line {
my \$coinpos = @coins[\$line - 1];

@coins[\$line] = do if not \$coinpos.defined {
Nil
} elsif hits-peg(\$coinpos, \$line) {
# when a coin from above hits a peg, it will bounce to either side.
\$alive = True;
(\$coinpos - 1, \$coinpos + 1).pick;
} else {
# if there was a coin above, it will fall to this position.
\$alive = True;
\$coinpos;
}
}
# let the coin dispenser blink and turn it off if we run out of coins
if @coins[0].defined {
@coins[0] = Nil
} elsif --\$coins > 0 {
@coins[0] = 0
}

# smooth out the two halfsteps of the animation
my \$start-time;
ENTER { \$start-time = now }
my \$wait-time = now - \$start-time;

sleep 0.1 - \$wait-time if \$wait-time < 0.1;
for @coin-icons.keys {
sleep \$wait-time max 0.1;
display-board(@coins, @stats, \$_);
}
}
}

sub MAIN(\$coins = 20, \$peg-lines = 6) {
\$row-count = \$peg-lines;
simulate(\$coins);
}
```

REXX

The REXX version displays an ASCII version of a working Galton box.

Balls are dropped continuously   (up to a number specified or the default),   the default is enough rows of
pins to fill the top   1/3   rows of the terminal screen.

```/*REXX pgm simulates Sir Francis Galton's box, aka: Galton Board, quincunx, bean machine*/
trace off                                        /*suppress any messages for negative RC*/
if !all(arg())  then exit                        /*Any documentation was wanted?   Done.*/
signal on halt                                   /*allow the user to  halt  the program.*/
parse arg rows balls freeze seed .               /*obtain optional arguments from the CL*/
if rows ==''  |  rows==","   then   rows=   0    /*Not specified?  Then use the default.*/
if balls==''  | balls==","   then  balls= 100    /* "      "         "   "   "     "    */
if freeze=='' | freeze==","  then freeze=   0    /* "      "         "   "   "     "    */
if datatype(seed, 'W')   then call random ,,seed /*Was a seed specified?  Then use seed.*/
pin  = '·';              ball = '☼'              /*define chars for a  pin  and a  ball.*/
parse value  scrsize()   with   sd  sw  .        /*obtain the terminal depth and width. */
if sd==0  then sd= 40                            /*Not defined by the OS?  Use a default*/
if sw==0  then sw= 80                            /* "     "     "  "   "    "  "    "   */
sd= sd - 3                                       /*define the usable       screen depth.*/
sw= sw - 1;  if sw//2  then sw= sw - 1           /*   "    "    "     odd     "   width.*/
if rows==0  then rows= (sw - 2 ) % 3             /*pins are on the first third of screen*/
call gen                                         /*gen a triangle of pins with some rows*/
do step=1;  call drop;  call show     /*show animation 'til run out of balls.*/
end   /*step*/                        /* [↑]  the dropping/showing   "   "   */
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: @.=;  do r=0  by 2  to rows;     \$=         /*build a triangle of pins for the box.*/
do pins=1  for r%2;   \$= \$  pin  /*build a row of pins to be displayed. */
end   /*pins*/
@.r= center( strip(\$, 'T'), sw)       /*an easy method to build a triangle.  */
end     /*r*/;     #= 0;       return /*#:   is the number of balls dropped. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
drop: static= 1                                  /*used to indicate all balls are static*/
do c=sd-1  by -1  for sd-1;    n= c + 1  /*D:  current row;   N:  the next row. */
x= pos(ball, @.c);             y= x - 1  /*X:  position of a ball on the C line.*/
if x==0  then iterate                    /*No balls here?  Then nothing to drop.*/
do forever;   y= pos(ball, @.c, y+1)   /*drop most balls down to the next row.*/
if y==0  then iterate c                /*down with this row, go look at next. */
z= substr(@.n, y, 1)                   /*another ball is blocking this fall.  */
if z==' '  then do;  @.n= overlay(ball, @.n, y)   /*drop a ball straight down.*/
@.c= overlay(' ' , @.c, y)   /*make current ball a ghost.*/
static= 0                    /*indicate balls are moving.*/
iterate                      /*go keep looking for balls.*/
end
if z==pin  then do;  ?= random(,999);   d= -1     /*assume falling to the left*/
if ?//2  then d=  1     /*if odd random#, fall right*/
if substr(@.n, y+d, 1)\==' '  then iterate /*blocked fall*/
@.n= overlay(ball, @.n, y+d)
@.c= overlay(' ' , @.c, y  )
static= 0                    /*indicate balls are moving.*/
iterate                      /*go keep looking for balls.*/
end
end   /*forever*/
end     /*c*/                  /* [↓]   step//2    is used to avoid collisions. */
/* [↓]  drop a new ball ?   */
if #<balls & step//2  then do;    @.1= center(ball, sw+1);      # = # + 1;        end
else if static  then exit 2      /*insure balls are static.  */
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: !cls;    do LR=sd  by -1  until @.LR\==''                 /*LR:  last row of data.*/
end   /*LR*/;                 ss= 'step' step    /* [↓]   display a row. */
do r=1  for LR; _= strip(@.r, 'T');  if r==2  then _= overlay(ss, _, sw-12); say _
end   /*r*/;   if step==freeze  then do;   say 'press ENTER ···';    pull;   end
return
/*══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════*/
halt:  say '***warning***  REXX program'   !fn    "execution halted by user.";      exit 1
!all:  !!=!;!=space(!);upper !;call !fid;!nt=right(!var('OS'),2)=='NT';!cls=word('CLS VMFCLEAR CLRSCREEN',1+!cms+!tso*2);if arg(1)\==1 then return 0;if wordpos(!,'? ?SAMPLES ?AUTHOR ?FLOW')==0 then return 0;!call=']\$H';call '\$H' !fn !;!call=;return 1
!cal:  if symbol('!CALL')\=="VAR"  then !call=;                                  return !call
!env:  !env='ENVIRONMENT';    if !sys=='MSDOS' | !brexx | !r4 | !roo  then !env= 'SYSTEM';    if !os2  then !env= 'OS2'!env;    !ebcdic=  2=='f2'x;    if !crx  then !env= 'DOS';                     return
!fid:  parse upper source !sys !fun !fid . 1 . . !fn !ft !fm .;  call !sys;   if !dos  then do;  _= lastpos('\', !fn);  !fm= left(!fn, _);  !fn= substr(!fn, _+1);  parse var !fn !fn '.' !ft;  end;  return word(0 !fn !ft !fm, 1 + ('0'arg(1) ) )
!rex:  parse upper version !ver !vernum !verdate .; !brexx= 'BY'==!vernum; !kexx= 'KEXX'==!ver; !pcrexx= 'REXX/PERSONAL'==!ver | 'REXX/PC'==!ver; !r4= 'REXX-R4'==!ver; !regina= 'REXX-REGINA'==left(!ver, 11); !roo= 'REXX-ROO'==!ver; call !env;  return
!sys:  !cms= !sys=='CMS';  !os2= !sys=='OS2';  !tso= !sys=='TSO' | !sys=='MVS';  !vse= !sys=='VSE';  !dos= pos('DOS', !sys)\==0 | pos('WIN', !sys)\==0 | !sys=='CMD';  !crx= left(!sys, 6)=='DOSCRX';  call !rex;  return
!var:  call !fid;  if !kexx  then return space( dosenv( arg(1) ) );              return space( value( arg(1), , !env) )
```

Programming note:   the last seven lines of this REXX program are some general purpose (boilerplate code) that, among other things, finds:

•   the REXX program's filename, filetype (file extension), and filemode (and/or path)
•   if the user wants documentation presented (not germane to this REXX program)
•   the environment name (not germane)
•   what command to be used to clear the terminal screen
•   the name of the operating system being used (not germane)
•   the name of the REXX interpreter being used (not germane)
•   various other bits of information (not germane)

It is only intended to be used to make this particular REXX program independent of any particular REXX interpreter and/or independent of knowing which program is to be used for clearing the terminal screen.   As such, the boilerplate code isn't commented and isn't intended to be a teaching tool.

This REXX program makes use of   SCRSIZE   REXX program (or BIF) which is used to determine the screen
width and depth of the terminal (console).   Some REXXes don't have this BIF.

The   SCRSIZE.REX   REXX program is included here   ───►   SCRSIZE.REX.

The terminal size used for this display was   64x96.

output   when the REXX program was "stopped" by using the inputs of     , , 100   so as to freeze the program to capture a screenshot:

(Shown at   2/3   size.)

```                                              ☼·                          step 100

·☼·

· ·☼·

· ·☼· ·

☼· · · · ·

· · ·☼· · ·

·☼· · · · · ·

· · · · ·☼· · ·

· · · · · · ·☼· ·

· · ·☼· · · · · · ·

· · · ·☼· · · · · · ·

· · · ·☼· · · · · · · ·

· · ·☼· · · · · · · · · ·

· · · · · · · ·☼· · · · · ·

· · · · · · ·☼· · · · · · · ·

☼

☼

☼

☼

☼

☼

☼

☼

☼

☼

☼

☼

☼

☼ ☼   ☼
☼ ☼   ☼
☼   ☼ ☼ ☼ ☼ ☼     ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼   ☼
press ENTER ···
```
output   when using the above inputs;   this is the final screenshot:

(Shown at   2/3   size.)

```                                               ·                          step 350

· ·

· · ·

· · · ·

· · · · ·

· · · · · ·

· · · · · · ·

· · · · · · · ·

· · · · · · · · ·

· · · · · · · · · ·

· · · · · · · · · · ·

· · · · · · · · · · · ·

· · · · · · · · · · · · ·

· · · · · · · · · · · · · ·

· · · · · · · · · · · · · · ·

☼
☼ ☼
☼ ☼
☼ ☼ ☼
☼ ☼ ☼
☼ ☼ ☼
☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼ ☼
```

Ruby

Library: Shoes
```\$rows_of_pins = 12
\$width = \$rows_of_pins * 10 + (\$rows_of_pins+1)*14

Shoes.app(
:width => \$width + 14,
:title => "Galton Box"
) do
@bins = Array.new(\$rows_of_pins+1, 0)

@x_coords = Array.new(\$rows_of_pins) {Array.new}
@y_coords = Array.new(\$rows_of_pins)
stack(:width => \$width) do
stroke gray
fill gray
1.upto(\$rows_of_pins) do |row|
y = 14 + 24*row
@y_coords[row-1] = y
row.times do |i|
x = \$width / 2 + (i - 0.5*row)*24 + 14
@x_coords[row-1] << x
oval x+2, y, 6
end
end
end
@y_coords << @y_coords[-1] + 24
@x_coords << @x_coords[-1].map {|x| x-12} + [@x_coords[-1][-1]+12]

@balls = stack(:width => \$width) do
stroke red
fill red
end.move(0,0)

@histogram = stack(:width => \$width) do
nostroke
fill black
end.move(0, @y_coords[-1] + 10)

@paused = false
keypress do |key|
case key
when "\x11", :control_q
exit
when "\x10", :control_p
@paused = !@paused
end
end

@ball_row = 0
@ball_col = 0
animate(2*\$rows_of_pins) do
if not @paused
y = @y_coords[@ball_row] - 12
x = @x_coords[@ball_row][@ball_col]
@balls.clear {oval x, y, 10}
@ball_row += 1
if @ball_row <= \$rows_of_pins
@ball_col += 1 if rand >= 0.5
else
@bins[@ball_col] += 1
@ball_row = @ball_col = 0
update_histogram
end
end
end

def update_histogram
y = @y_coords[-1] + 10
@histogram.clear do
@bins.each_with_index do |num, i|
if num > 0
x = @x_coords[-1][i]
rect x-6, 0, 24, num
end
end
end
end
end
```

Tcl

Translation of: C
```package require Tcl 8.6

oo::class create GaltonBox {
variable b w h n x y cnt step dropping

constructor {BALLS {NUMPEGS 5} {HEIGHT 24}} {
set n \$NUMPEGS
set w [expr {\$n*2 + 1}]
set h \$HEIGHT
puts -nonewline "\033\[H\033\[J"
set x [set y [lrepeat \$BALLS 0]]
set cnt 0
set step 0
set dropping 1

set b [lrepeat \$h [lrepeat \$w " "]]
for {set i 0} {\$i < \$n} {incr i} {
for {set j [expr {-\$i}]} {\$j <= \$i} {incr j 2} {
lset b [expr {2*\$i+2}] [expr {\$j+\$w/2}] "*"
}
}
}

method show {} {
puts -nonewline "\033\[H"
set oldrow {}
foreach row \$b {
foreach char \$row oldchar \$oldrow {
if {\$char ne "*"} {
puts -nonewline "\$char "
} elseif {\$oldchar eq " "} {
puts -nonewline "\033\[32m*\033\[m "
} else {
puts -nonewline "\033\[31m*\033\[m "
}
}
set oldrow \$row
puts ""
}
}

method Move idx {
set xx [lindex \$x \$idx]
set yy [lindex \$y \$idx]
set kill 0

if {\$yy < 0} {return 0}
if {\$yy == \$h-1} {
lset y \$idx -1
return 0
}

switch [lindex \$b [incr yy] \$xx] {
"*" {
incr xx [expr {2*int(2 * rand()) - 1}]
if {[lindex \$b [incr yy -1] \$xx] ne " "} {
set dropping 0
}
}
"o" {
incr yy -1
set kill 1
}
}

set c [lindex \$b [lindex \$y \$idx] [lindex \$x \$idx]]
lset b [lindex \$y \$idx] [lindex \$x \$idx] " "
lset b \$yy \$xx \$c
if {\$kill} {
lset y \$idx -1
} else {
lset y \$idx \$yy
}
lset x \$idx \$xx
return [expr {!\$kill}]
}

method step {} {
set moving 0
for {set i 0} {\$i < \$cnt} {incr i} {
set moving [expr {[my Move \$i] || \$moving}]
}
if {2 == [incr step] && \$cnt < [llength \$x] && \$dropping} {
set step 0
lset x \$cnt [expr {\$w / 2}]
lset y \$cnt 0
if {[lindex \$b [lindex \$y \$cnt] [lindex \$x \$cnt]] ne " "} {
return 0
}
lset b [lindex \$y \$cnt] [lindex \$x \$cnt] "o"
incr cnt
}
return [expr {(\$moving || \$dropping)}]
}
}

GaltonBox create board 1024 {*}\$argv
while true {
board show
if {[board step]} {after 60} break
}
```

After a sample run with input parameters 10 55:

```

*

*   *

*   *   *

*   *   *   *

*   *   *   *   *

*   *   *   *   *   *

*   *   *   *   *   *   *

*   *   *   *   *   *   *   *

*   *   *   *   *   *   *   *   *
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
o   o   o   o   o   o   o   o
o   o   o   o   o   o   o   o
```

There is a much more comprehensive solution to this on the Tcler's Wiki.

Wren

Translation of: D
Library: Wren-iterate
```import "random" for Random
import "./iterate" for Reversed

var boxW = 41       // Galton box width.
var boxH = 37       // Galton box height.
var pinsBaseW = 19  // Pins triangle base.
var nMaxBalls = 55  // Number of balls.

var centerH = pinsBaseW + (boxW - pinsBaseW * 2 + 1) / 2 - 1
var Rand = Random.new()

class Cell {
static EMPTY  { " " }
static BALL   { "o" }
static WALL   { "|" }
static CORNER { "+" }
static FLOOR  { "-" }
static PIN    { "." }
}

/* Galton box. Will be printed upside down. */
var Box = List.filled(boxH, null)
for (i in 0...boxH) Box[i] = List.filled(boxW, Cell.EMPTY)

class Ball {
construct new(x, y) {
if (Box[x][y] != Cell.EMPTY) Fiber.abort("The cell at (x, y) is not empty.")
Box[y][x] = Cell.BALL
_x = x
_y = y
}

doStep() {
if (_y <= 0) return  // Reached the bottom of the box.
var cell = Box[_y - 1][_x]
if (cell == Cell.EMPTY) {
Box[_y][_x] = Cell.EMPTY
_y = _y - 1
Box[_y][_x] = Cell.BALL
} else if (cell == Cell.PIN) {
Box[_y][_x] = Cell.EMPTY
_y = _y - 1
if (Box[_y][_x - 1] == Cell.EMPTY && Box[_y][_x + 1] == Cell.EMPTY) {
_x = _x + Rand.int(2) * 2 - 1
Box[_y][_x] = Cell.BALL
return
} else if (Box[_y][_x - 1] == Cell.EMPTY){
_x = _x + 1
} else _x = _x - 1
Box[_y][_x] = Cell.BALL
} else {
// It's frozen - it always piles on other balls.
}
}
}

var initializeBox = Fn.new {
// Set ceiling and floor:
Box[0][0] = Cell.CORNER
Box[0][boxW - 1] = Cell.CORNER
for (i in 1...boxW - 1) Box[0][i] = Cell.FLOOR
for (i in 0...boxW) Box[boxH - 1][i] = Box[0][i]

// Set walls:
for (r in 1...boxH - 1) {
Box[r][0] = Cell.WALL
Box[r][boxW - 1] = Cell.WALL
}

// Set pins:
for (nPins in 1..pinsBaseW) {
for (pin in 0...nPins) {
Box[boxH - 2 - nPins][centerH + 1 - nPins + pin * 2] = Cell.PIN
}
}
}

var drawBox = Fn.new() {
for (row in Reversed.new(Box, 1)) {
for (c in row) System.write(c)
System.print()
}
}

initializeBox.call()
var balls = []
for (i in 0...nMaxBalls + boxH) {
System.print("\nStep %(i):")
drawBox.call()

// Next step for the simulation.
// Frozen balls are kept in balls list for simplicity
for (b in balls) b.doStep()
}
```
Output:

Sample output, showing the last step only:

```Step 91:
+---------------------------------------+
|                                       |
|                   .                   |
|                  . .                  |
|                 . . .                 |
|                . . . .                |
|               . . . . .               |
|              . . . . . .              |
|             . . . . . . .             |
|            . . . . . . . .            |
|           . . . . . . . . .           |
|          . . . . . . . . . .          |
|         . . . . . . . . . . .         |
|        . . . . . . . . . . . .        |
|       . . . . . . . . . . . . .       |
|      . . . . . . . . . . . . . .      |
|     . . . . . . . . . . . . . . .     |
|    . . . . . . . . . . . . . . . .    |
|   . . . . . . . . . . . . . . . . .   |
|  . . . . . . . . . . . . . . . . . .  |
| . . . . . . . . . . . . . . . . . . . |
|                                       |
|                                       |
|                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      |
+---------------------------------------+
```

XPL0

This Peeks into some IBM-PC specific locations and hence is not entirely portable.

```include c:\cxpl\codes;          \intrinsic code declarations
define  Balls = 80;             \maximum number of balls
int     Bx(Balls), By(Balls),   \character cell coordinates of each ball
W, I, J, Peg, Dir;
[W:= Peek(\$40, \$4A);            \get screen width in characters
Clear;  CrLf(6);  CrLf(6);
for Peg:= 1 to 10 do                            \draw pegs
[for I:= 1 to 12-Peg do ChOut(6,^ );    \space over to first peg
for I:= 1 to Peg do [ChOut(6,^.);  ChOut(6,^ )];
CrLf(6);
];
for J:= 0 to 12-1 do                            \draw slots
[for I:= 0 to 12-1 do [ChOut(6,^:);  ChOut(6,^ )];
CrLf(6);
];
for I:= 0 to 23-1 do ChOut(6,^.);               \draw bottom
for I:= 0 to Balls-1 do                         \make source of balls at top
[Bx(I):= 11;  By(I):= 1];
Attrib(\$C);                                     \make balls bright red
repeat                                          \balls away! ...
for I:= 0 to Balls-1 do                     \for all the balls ...
[Cursor(Bx(I), By(I));  ChOut(6, ^ );   \erase ball's initial position
if Peek(\$B800, (Bx(I)+(By(I)+1)*W)*2) = ^ \is ball above empty location?
then    By(I):= By(I)+1                 \yes: fall straight down
else    [Dir:= Ran(3)-1;                \no: randomly fall right or left
if Peek(\$B800, (Bx(I)+Dir+(By(I)+1)*W)*2) = ^  then
[Bx(I):= Bx(I)+Dir;  By(I):= By(I)+1];
];
Cursor(Bx(I), By(I));  ChOut(6, ^o);    \draw ball at its new position
];
Sound(0, 3, 1);                             \delay about 1/6 second
until KeyHit;                                   \continue until a key is struck
]```
Output:
```           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: : : :
.......................
```

Yabasic

```bola\$ = "0000ff"
obst\$ = "000000"

maxBalls = 10
cx = 1
cy = 2
dim Balls(maxBalls, 2)

open window 600,600
window origin "ct"

maxh = peek("winheight")

REM Draw the pins:

FOR row = 1 TO 7
FOR col = 1 TO row
FILL circle 40*col - 20*row, 40*row+80, 10
NEXT col
NEXT row

REM Animate
tick = 0
bolas = 0
color 0,0,255

do
if (bolas < maxBalls) then
if tick = 3 then
tick = 0
bolas = bolas + 1
Balls(bolas, cx) = 20
Balls(bolas, cy) = 10
end if
tick = tick + 1
end if
for n = 1 to bolas
if Balls(n, cy) then
color\$ = right\$(getbit\$(Balls(n,cx),Balls(n,cy) + 10,Balls(n,cx),Balls(n,cy) + 10),6)
if (color\$ = bola\$) or (Balls(n,cy) >= maxh - 15) then
Balls(n,cy) = 0
break
end if
clear fill circle Balls(n,cx),Balls(n,cy),10
if color\$ = obst\$ then
if int(ran(2)) then
Balls(n,cx) = Balls(n,cx) - 20
else
Balls(n,cx) = Balls(n,cx) + 20
end if
end if
Balls(n,cy) = Balls(n,cy)+10
fill circle Balls(n,cx),Balls(n,cy),10
wait .001
else
wait .001
end if
next n
loop```

Zig

```const std = @import("std");
const rand = std.rand;
const time = std.time;

const PEG_LINES = 20;
const BALLS = 10;

fn boardSize(comptime peg_lines: u16) u16 {
var i: u16 = 0;
var size: u16 = 0;
inline while (i <= peg_lines) : (i += 1) {
size += i + 1;
}
return size;
}

const BOARD_SIZE = boardSize(PEG_LINES);

fn stepBoard(board: *[BOARD_SIZE]u1, count: *[PEG_LINES + 1]u8) void {
var prng = rand.DefaultPrng.init(@bitCast(time.timestamp()));

var p: u8 = 0;
var sum: u16 = 0;
while (p <= PEG_LINES) : (p += 1) {
const pegs = PEG_LINES - p;
var i: u16 = 0;
while (i < pegs + 1) : (i += 1) {
if (pegs != PEG_LINES and board[BOARD_SIZE - 1 - sum - i] == 1) {
if (prng.random().boolean()) {
board.*[BOARD_SIZE - 1 - sum - i + pegs + 1] = 1;
} else {
board.*[BOARD_SIZE - 1 - sum - i + pegs + 2] = 1;
}
} else if (pegs == PEG_LINES and board[BOARD_SIZE - 1 - sum - i] == 1) {
count.*[pegs - i] += 1;
}
board.*[BOARD_SIZE - 1 - sum - i] = 0;
}
sum += pegs + 1;
}
}

fn printBoard(board: *[BOARD_SIZE]u1, count: *[PEG_LINES + 1]u8) !void {
const stdout = std.io.getStdOut();
_ = try stdout.write("\x1B[2J\x1B[1;1H");
var pegs: u16 = 0;
var sum: u16 = 0;
while (pegs <= PEG_LINES) : (pegs += 1) {
var i: u16 = 0;
while (i < (PEG_LINES - pegs)) : (i += 1) _ = try stdout.write(" ");
i = 0;
while (i < pegs + 1) : (i += 1) {
const spot = if (board[i + sum] == 1) "o" else " ";
_ = try stdout.write(spot);
if (i != pegs) _ = try stdout.write("*");
}
sum += pegs + 1;
_ = try stdout.write("\n");
}
for (count) |n| {
const num_char = [2]u8{'0' + n, ' '};
_ = try stdout.write(&num_char);
}
_ = try stdout.write("\n");
}

pub fn main() !void {
var board: [BOARD_SIZE]u1 = [_]u1{0} ** BOARD_SIZE;
var bottom_count: [PEG_LINES+1]u8 = [_]u8{0} ** (PEG_LINES + 1);

var i: u16 = 0;
while (i < PEG_LINES + BALLS + 1) : (i += 1) {
if (i < BALLS) board[0] = 1;

try printBoard(&board, &bottom_count);
stepBoard(&board, &bottom_count);
time.sleep(150000000);
}
}
```