Galton box animation: Difference between revisions
m (provided a URL to a bell curve.) |
m (→gui: IupCloseOnEscape no longer needed) |
||
| Line 2,878: | Line 2,878: | ||
dlg = IupDialog(canvas) |
dlg = IupDialog(canvas) |
||
IupSetAttribute(dlg, "TITLE", TITLE) |
IupSetAttribute(dlg, "TITLE", TITLE) |
||
IupCloseOnEscape(dlg) |
|||
IupShow(dlg) |
IupShow(dlg) |
||
IupSetAttribute(canvas, "RASTERSIZE", NULL) |
IupSetAttribute(canvas, "RASTERSIZE", NULL) |
||
Revision as of 21:21, 25 January 2021
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.
- Task
Generate an animated simulation of a Galton device.
- Task requirements
-
- 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 <lang AutoHotkey>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" . pad2 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 ballX += RandAdd() ; 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 "" } RandAdd(){ 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 }</lang>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
<lang 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)
rad = 6 slow = 0.3 diamond = {0,rad,rad,0,0,-rad,-rad,0} stepx = {rad/sqr(2),rad/2,rad/2,(1-1/sqr(2))*rad,0} stepy = {(1-1/sqr(2))*rad,rad/2,rad/2,rad/sqr(2),rad} CX = graphwidth/2 : CY = graphheight/2 iters = 0
- Draw pins
for i = 1 to M y = 3*rad*i for j = 1 to i dx = (j-i\2-1)*4*rad + ((i-1)%2)*2*rad 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 y = 3*rad*(M+1) for j = 0 to M dx = (j-(M+1)\2)*4*rad + (M%2)*2*rad stamp CX+dx,y,{-1.2*rad,0,1.2*rad,0,1.2*rad,2*cnt[j],-1.2*rad,2*cnt[j]} 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 ball[b,3] = ball[b,3]+rad end if gosub drawball
drawball: color darkgreen circle ball[b,2],ball[b,3],rad-1 color green circle ball[b,2],ball[b,3],rad-2 return
eraseball: color black circle ball[b,2],ball[b,3],rad-1 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</lang>
BBC BASIC
<lang bbcbasic> 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</lang>
C
<lang 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; }</lang>
Sample out put at begining of a run:
*
* *
* * *
* * * *
* * * * *
C++
Windows GDI version. <lang cpp>
- 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.biSize = sizeof( bi.bmiHeader );
bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
bi.bmiHeader.biCompression = BI_RGB;
bi.bmiHeader.biPlanes = 1;
bi.bmiHeader.biWidth = w;
bi.bmiHeader.biHeight = -h;
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 );
AdjustWindowRect( &rc, WS_CAPTION, FALSE );
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 );
} </lang>
D
To keep the code simpler some corner cases are ignored. <lang d>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;
}
}</lang>
- 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 | +---------------------------------------+
Elm
<lang 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 radius = hscale/ 2.0
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 addToBins binNumber bins =
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
}</lang>
Link to live demo: http://dc25.github.io/galtonBoxAnimationElm/ . Follow the link, enter a number and press the GO button.
Factor
<lang factor>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-gadget> ( -- gadget )
galton new bg-color <solid> >>interior V{ } clone >>balls
dup [ on-tick ] curry f speed milliseconds <timer>
start-timer ;
- add-ball ( gadget -- )
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 } ;
M: galton draw-gadget*
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 } }
} <galton-gadget> >>gadgets ;</lang>
- Output:
Image taken from the program mid-animation: [1]
![[1]](https://i.imgur.com/E2ge7LE.png){kind=link}
Go
<lang go>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()
}
}
}</lang>
- 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 | +---------------------------------------+
Haskell
<lang haskell>import Data.Map hiding (map, filter) import Graphics.Gloss import Control.Monad.Random
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)</lang>
Icon and Unicon
The code here is adapted from the Unicon Book.
<lang Icon>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</lang>
J
First, we need to represent our pins:
<lang j>initpins=: '* ' {~ '1'&i.@(-@|. |."_1 [: ":@-.&0"1 <:~/~)@i.</lang>
For example:
<lang j> initpins 4
* * * * * *
- * * *</lang>
Note that we could introduce other pin arrangements, for example a Sierpinski triangle:
<lang j>initSpins=: [: }.@|. (1- 2&^@>:) ]\ [: ,] (,~ ,.~)@]^:[ ,: bind '* '</lang>
... 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:
<lang j>init=: ' ',. ' ',.~ ] ,~ ' ',~ ' o' {~ (# ' ' ~: 1&{.)</lang>
For example:
<lang j> 3 (init initpins) 4
o
o
o
*
* *
* * *
* * * * </lang>
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:
<lang>bounce=: (C.~ ] <"1@:+ 0 1 -~/~ ? @: (2"0))"1 [: I. 'o*'&E."1&.|:</lang>
And, a mechanism to make the balls fall:
<lang>shift=: 4 :0
fill=. {.0#,y
x |.!.fill y
)</lang>
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.
<lang j>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</lang>
For example:
<lang j> nxt nxt 3 (init initpins) 4
o
o
o*
* *
* * *
* * * *
</lang>
Or, showing an entire animation sequence:
<lang j> 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 │ │ * * * │ * * * │ * * * * │ * * * * * │ │ │ │ │ │ │ │ │ │ │ │ * * * * │ * * * * │ * * * * * │ │ │ │ │ │ │ │ │ │ │ │ │ * * * * * │ * * * * * │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘</lang>
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... <lang Java>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>();
collectors.add( collector );
for ( int ball = 0; ball < m_balls.length; ball++ )
if ( m_balls[ ball ].m_row == 0 && m_balls[ ball ].m_col == col )
collector.add( m_balls[ ball ] );
}
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; }
}</lang>
- 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 <lang JavaScript>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 = () => {
readline.cursorTo(process.stdout, 0, 0);
readline.clearScreenDown(process.stdout);
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 () => {
while (addBall()) {
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);</lang>
- 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.
<lang julia>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</lang>
- 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
<lang scala>// 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:")
if (i < nMaxBalls) balls.add(Ball(centerH, boxH - 2)) // Add ball.
drawBox()
// Next step for the simulation.
// Frozen balls are kept in balls list for simplicity
for (b in balls) b.doStep()
}
}</lang>
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. <lang lb> [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"
'add sprites to program
for pinCount = 1 to 28
#1 "addsprite pin";pinCount;" pin;spriteround pin";pinCount
next pinCount
for ballCount = 1 to 7
#1 "addsprite ball";ballCount;" ball;spriteround ball";ballCount
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 unloadbmp "pin" unloadbmp "ball" unloadbmp "bg" end
</lang>
Nim
<lang Nim>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. discard
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: balls.add box.newBall(CenterH, BoxH - 2) box.draw()
# Next step for the simulation. # Frozen balls are kept in balls slice for simplicity. for ball in balls: box.doStep(ball)</lang>
- 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.
<lang perl>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
my $padding = 0;
while (any {$_> 0} @stats) {
$padding++;
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("");
}
printnl("") for $padding..(10-1);
}
print join(, @output) . "\n";
}
sub hits_peg {
my($x, $y) = @_;
3 <= $y && $y < (3 + $row_count) and -($y - 2) <= $x && $x <= $y - 2
? not 0 == ($x - $y) % 2
: 0
}</lang>
- Output:
^
^ ^
^ ^ ^
^ ^ ^ ^
^ ^ ^ ^ ^
^ ^ ^ ^ ^ ^
^ ^ ^ ^ ^ ^ ^
█ █ █ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ ▀
▀ █ █
█
native Perl
Runs until a bottom column overflows. <lang perl>#!/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;
}</lang>
- 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: <lang Phix>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</lang>
- 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:
<lang Phix>-- demo\rosetta\GaltonBox.exw constant TITLE = "Galton Box"
include pGUI.e
Ihandle dlg, canvas, timershow cdCanvas cddbuffer, cdcanvas
integer brem = 80 sequence balls = Template:0,1,0 sequence bins = repeat(0,8)
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*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
cdCanvasLineWidth(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
bins[(x+18)/4] += 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(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "640x380")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
timershow = IupTimer(Icallback("timer_cb"), 80)
dlg = IupDialog(canvas) IupSetAttribute(dlg, "TITLE", TITLE) IupShow(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) IupMainLoop() IupClose()
end procedure
main()</lang>
PicoLisp
<lang 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) ) ) )</lang>
Test: <lang PicoLisp>(galtonBox 9 11)</lang>
- 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.
<lang Prolog>:- 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), message(@receiver, destroy))), 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 add_ball(P) :-> 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 unlink(P) :-> send(P?mytimer, stop), send(P, send_super, unlink).
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), send(Tube, add_ball), 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))). </lang>
PureBasic
<lang purebasic>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)
CanvasGadget(0, 0, 0, width, height)
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 pegRadius = 4 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</lang>
Python
<lang 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)
def add_ball(self):
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)
board.add_ball() #initialization
while(board.balls_on_board() > 0):
board.print_all()
time.sleep(0.25)
board.update()
board.print_all()
time.sleep(0.25)
board.update()
board.add_ball()
if __name__=="__main__":
main()</lang>
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.
<lang Racket>
- 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))))
(define BALL-RADIUS 6)
- 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-WH (* 2 BALL-RADIUS)) (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")
(circle BALL-RADIUS "solid" "dark 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)
(make-pos (add1 (pos-row 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)))))
</lang>
Raku
(formerly Perl 6)
<lang perl6>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
my $padding = 0;
while any(@stats) > 0 {
$padding++;
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 "" for $padding...^10;
}
say @output.join("");
}
sub simulate($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);
}</lang>
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.
<lang rexx>/*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) )</lang> 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
<lang ruby>$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</lang>
Tcl
<lang tcl>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
}</lang> 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.
XPL0
This Peeks into some IBM-PC specific locations and hence is not entirely portable.
<lang XPL0>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 ]</lang>
- 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
<lang 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 </lang>
zig
<lang zig>const std = @import("std"); const rand = std.rand; const time = std.os.time;
const PEG_LINES = 20;
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(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 {
var stdout = try 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 < 35) : (i += 1) {
if (i < 10) board[0] = 1;
try printBoard(&board, &bottom_count);
stepBoard(&board, &bottom_count);
time.sleep(150000000);
}
}</lang>