Galton box animation
You are encouraged to solve this task according to the task description, using any language you may know.
Generate an animated simulation of Sir Francis Galton's device. An example can be found to the right.
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 subsequent pins before arriving at one of the collection points between and to the sides of the bottom row of pins.
For the purpose of this task the box should have at least 5 pins on the bottom row. Your solution can use graphics or ASCII animation. Provide a sample of the output/display such as a screenshot.
Your solution can have either one or more balls in flight at the same time. If multiple balls are in flight, ensure they don't interfere with each other.
Your 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
FOR r% = 1 TO 7
IF ballY%(ball%) = 820 - 40*r% ballX%(ball%) += 40 * (RND(2) - 1.5)
NEXT
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:
*
* *
* * *
* * * *
* * * * *
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 a representation for 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 sufficiently deep to hold the stacks and have balls instantly fall as close as they can to the baseline once they are past 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>
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, $EB))
For i = 1 To numRows
ypos = i * pegSize2
xpos = width / 2 - (i - 1) * pegSize - pegSize / 2
For j = 1 To i
Circle(xpos, ypos, pegRadius, RGB(0, 0, 255))
xpos + pegSize2
Next
Next
For i = 1 To numRows
Line((numRows - i + 1) * pegSize2 - pegSize / 2, width - pegSize, 1, histogramSize * pegSize, 0)
Next
StopDrawing()
EndProcedure
- based on the galton box simulation from Unicon book
Define pegRows = 10, ballCount pegRadius = 4 pegSize = pegRadius * 2 + 1 pegSize2 = pegSize * 2 delay = 2 ; ms delay
Repeat
ballCount = Val(InputRequester("Galton box simulator","How many balls to drop?", "100"))
Until ballCount > 0
setup_window(pegRows, ballCount) eventLoop() For ball = 1 To ballCount
If Not galton(pegRows): Break: EndIf
Next Repeat: eventLoop(): ForEver</lang>
Ruby
<lang ruby>$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>
Example 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: : : :
.......................