Brownian tree
| This page uses content from Wikipedia. The original article was at Brownian_tree. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
You are encouraged to solve this task according to the task description, using any language you may know.
Generate and draw a Brownian Tree.
A Brownian Tree is generated as a result of an initial seed, followed by the interaction of two processes.
- The initial "seed" is placed somewhere within the field. Where is not particularly important; it could be randomized, or it could be a fixed point.
- Particles are injected into the field, and are individually given a (typically random) motion pattern.
- When a particle collides with the seed or tree, its position is fixed, and it's considered to be part of the tree.
Because of the lax rules governing the random nature of the particle's placement and motion, no two resulting trees are really expected to be the same, or even necessarily have the same general shape.
AutoHotkey
Takes a little while to run, be patient. Requires the GDI+ Standard Library by Tic <lang AHK>SetBatchLines -1 Process, Priority,, high size := 400 D := .08 num := size * size * d field:= Object() field[size//2, size//2] := true ; set the seed lost := 0
Loop % num { x := Rnd(1, size), y := Rnd(1, size) Loop { oldX := X, oldY := Y x += Rnd(-1, 1), y += Rnd(1, -1) If ( field[x, y] ) { field[oldX, oldY] := true break } If ( X > Size ) or ( Y > Size) or ( X < 1 ) or ( Y < 1 ) { lost++ break } } }
pToken := Gdip_startup() pBitmap := Gdip_CreateBitmap(size, size) loop %size% { x := A_index Loop %size% { If ( field[x, A_Index] ) { Gdip_SetPixel(pBitmap, x, A_Index, 0xFF0000FF) } } } Gdip_SaveBitmapToFile(pBitmap, "brownian.png") Gdip_DisposeImage(pBitmap) Gdip_Shutdown(pToken) Run brownian.png
MsgBox lost %lost%
Rnd(min, max){ Random, r, min, max return r }</lang>Sample output file here
BBC BASIC
<lang bbcbasic> SYS "SetWindowText", @hwnd%, "Brownian Tree"
SIZE = 400
VDU 23,22,SIZE;SIZE;8,16,16,0
GCOL 10
REM set the seed:
PLOT SIZE, SIZE
OFF
REPEAT
REM set particle's initial position:
REPEAT
X% = RND(SIZE)-1
Y% = RND(SIZE)-1
UNTIL POINT(2*X%,2*Y%) = 0
REPEAT
oldX% = X%
oldY% = Y%
X% += RND(3) - 2
Y% += RND(3) - 2
UNTIL POINT(2*X%,2*Y%)
IF X%>=0 IF X%<SIZE IF Y%>=0 IF Y%<SIZE PLOT 2*oldX%,2*oldY%
UNTIL FALSE
</lang>
C
<lang c>#include <string.h>
- include <stdlib.h>
- include <time.h>
- include <math.h>
- include <FreeImage.h>
- define NUM_PARTICLES 1000
- define SIZE 800
void draw_brownian_tree(int world[SIZE][SIZE]){
int px, py; // particle values int dx, dy; // offsets int i; // set the seed world[rand() % SIZE][rand() % SIZE] = 1;
for (i = 0; i < NUM_PARTICLES; i++){
// set particle's initial position
px = rand() % SIZE;
py = rand() % SIZE;
while (1){
// randomly choose a direction
dx = rand() % 3 - 1;
dy = rand() % 3 - 1;
if (dx + px < 0 || dx + px >= SIZE || dy + py < 0 || dy + py >= SIZE){
// plop the particle into some other random location
px = rand() % SIZE;
py = rand() % SIZE;
}else if (world[py + dy][px + dx] != 0){
// bumped into something
world[py][px] = 1;
break;
}else{
py += dy;
px += dx;
}
}
}
}
int main(){
int world[SIZE][SIZE]; FIBITMAP * img; RGBQUAD rgb; int x, y; memset(world, 0, sizeof world); srand((unsigned)time(NULL));
draw_brownian_tree(world);
img = FreeImage_Allocate(SIZE, SIZE, 32, 0, 0, 0);
for (y = 0; y < SIZE; y++){
for (x = 0; x < SIZE; x++){
rgb.rgbRed = rgb.rgbGreen = rgb.rgbBlue = (world[y][x] ? 255 : 0);
FreeImage_SetPixelColor(img, x, y, &rgb);
}
}
FreeImage_Save(FIF_BMP, img, "brownian_tree.bmp", 0);
FreeImage_Unload(img);
}</lang> Bold text
Alternative Version
This version writes the image as Portable Bit Map to stdout and doesn't move already set particles. <lang c>#include <stdio.h>
- include <stdlib.h>
- include <time.h>
- include <stdbool.h>
- define SIDE 600
- define NUM_PARTICLES 10000
bool W[SIDE][SIDE];
int main() {
srand((unsigned)time(NULL)); W[SIDE / 2][SIDE / 2] = true;
for (int i = 0; i < NUM_PARTICLES; i++) {
unsigned int x, y;
OVER: do {
x = rand() % (SIDE - 2) + 1;
y = rand() % (SIDE - 2) + 1;
} while (W[y][x]);
while (W[y-1][x-1] + W[y-1][x] + W[y-1][x+1] +
W[y][x-1] + W[y][x+1] +
W[y+1][x-1] + W[y+1][x] + W[y+1][x+1] == 0) {
unsigned int dxy = rand() % 8;
if (dxy > 3) dxy++;
x += (dxy % 3) - 1;
y += (dxy / 3) - 1;
if (x < 1 || x >= SIDE - 1 || y < 1 || y >= SIDE - 1)
goto OVER;
}
W[y][x] = true; }
printf("P1\n%d %d\n", SIDE, SIDE);
for (int r = 0; r < SIDE; r++) {
for (int c = 0; c < SIDE; c++)
printf("%d ", W[r][c]);
putchar('\n');
}
return 0;
}</lang> Run-time about 12.4 seconds with SIDE=600, NUM_PARTICLES=10000.
C#
<lang csharp>using System; using System.Drawing;
namespace BrownianTree {
class Program
{
static Bitmap BrownianTree(int size, int numparticles)
{
Bitmap bmp = new Bitmap(size, size);
Rectangle bounds = new Rectangle { X = 0, Y = 0, Size = bmp.Size };
using (Graphics g = Graphics.FromImage(bmp))
{
g.Clear(Color.Black);
}
Random rnd = new Random();
bmp.SetPixel(rnd.Next(size), rnd.Next(size), Color.White);
Point pt = new Point(), newpt = new Point();
for (int i = 0; i < numparticles; i++)
{
pt.X = rnd.Next(size);
pt.Y = rnd.Next(size);
do
{
newpt.X = pt.X + rnd.Next(-1, 2);
newpt.Y = pt.Y + rnd.Next(-1, 2);
if (!bounds.Contains(newpt))
{
pt.X = rnd.Next(size);
pt.Y = rnd.Next(size);
}
else if (bmp.GetPixel(newpt.X, newpt.Y).R > 0)
{
bmp.SetPixel(pt.X, pt.Y, Color.White);
break;
}
else
{
pt = newpt;
}
} while (true);
}
return bmp;
}
static void Main(string[] args)
{
BrownianTree(300, 3000).Save("browniantree.png");
}
}
}</lang>
D
Partial
Writes a Portable Bit Map image to stdout. <lang d>import core.stdc.stdio, std.random;
enum uint side = 600; enum uint num_particles = 10_000; static assert(side > 2 && num_particles < (side ^^ 2 * 0.7));
void main() {
auto rng = Xorshift(unpredictableSeed); bool[side][side] W; // world W[side / 2][side / 2] = true; // set tree root
foreach (_; 0 .. num_particles) {
// random initial particle position
OVER: uint x, y;
do {
x = uniform(1, side - 1, rng);
y = uniform(1, side - 1, rng);
} while (W[y][x]); // assure the chosen cell is empty
while (W[y-1][x-1] + W[y-1][x] + W[y-1][x+1] +
W[y][x-1] + W[y][x+1] +
W[y+1][x-1] + W[y+1][x] + W[y+1][x+1] == 0) {
// randomly choose a direction (Moore neighborhood)
uint dxy = uniform(0, 8, rng);
if (dxy > 3) dxy++; // to avoid the center
x += (dxy % 3) - 1;
y += (dxy / 3) - 1;
if (x < 1 || x >= side - 1 || y < 1 || y >= side - 1)
goto OVER;
}
W[y][x] = true; // touched, set the cell }
// send PBM image to stdout
printf("P1\n%d %d\n", side, side);
foreach (ref line; W) {
foreach (pixel; line)
printf("%d ", pixel);
putchar('\n');
}
}</lang> One output, world side = 25, num_particles = 80:
P1 25 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
World side = 600, num_particles = 10_000, cropped, about 20 seconds run-time:
Delphi
<lang delphi>const
SIZE = 256; NUM_PARTICLES = 1000;
procedure TForm1.Button1Click(Sender: TObject); type
TByteArray = array[0..0] of Byte; PByteArray = ^TByteArray;
var
B: TBitmap; I: Integer; P, D: TPoint;
begin
Randomize;
B := TBitmap.Create;
try
B.Width := SIZE;
B.Height := SIZE;
B.PixelFormat := pf8bit;
B.Canvas.Brush.Color := clBlack;
B.Canvas.FillRect(B.Canvas.ClipRect);
B.Canvas.Pixels[Random(SIZE), Random(SIZE)] := clWhite;
For I := 0 to NUM_PARTICLES - 1 do
Begin
P.X := Random(SIZE);
P.Y := Random(SIZE);
While true do
Begin
D.X := Random(3) - 1;
D.Y := Random(3) - 1;
Inc(P.X, D.X);
Inc(P.Y, D.Y);
If ((P.X or P.Y) < 0) or (P.X >= SIZE) or (P.Y >= SIZE) Then
Begin
P.X := Random(SIZE);
P.Y := Random(SIZE);
end
else if PByteArray(B.ScanLine[P.Y])^[P.X] <> 0 then
begin
PByteArray(B.ScanLine[P.Y-D.Y])^[P.X-D.X] := $FF;
Break;
end;
end;
end;
Canvas.Draw(0, 0, B);
finally
FreeAndNil(B);
end;
end;</lang>
Fantom
<lang fantom> using fwt using gfx
class Main {
public static Void main ()
{
particles := Particles (300, 200)
1000.times { particles.addParticle } // add 1000 particles
Window // open up a display for the final tree
{
title = "Brownian Tree"
EdgePane
{
center = ScrollPane { content = ParticleCanvas(particles) }
},
}.open
}
}
class Particles {
Bool[][] image Int height Int width
new make (Int height, Int width)
{
this.height = height
this.width = width
// set up initial image as an array of booleans with one set cell
image = [,]
width.times |w|
{
row := [,]
height.times { row.add (false) }
image.add (row)
}
image[Int.random(0..<width)][Int.random(0..<height)] = true
}
Bool get (Int w, Int h) { return image[w][h] }
Void addParticle ()
{
x := Int.random(0..<width)
y := Int.random(0..<height)
Int dx := 0
Int dy := 0
while (!image[x][y]) // loop until hit existing part of the tree
{
dx = [-1,0,1].random
dy = [-1,0,1].random
if ((0..<width).contains(x + dx))
x += dx
else // did not change x, so set dx = 0
dx = 0
if ((0..<height).contains(y + dy))
y += dy
else
dy = 0
}
// put x,y back to just before move onto existing part of tree x -= dx y -= dy
image[x][y] = true }
}
class ParticleCanvas : Canvas {
Particles particles
new make (Particles particles) { this.particles = particles }
// provides canvas size for parent scrollpane
override Size prefSize(Hints hints := Hints.defVal)
{
Size(particles.width, particles.height)
}
// repaint the display
override Void onPaint (Graphics g)
{
g.brush = Color.black
g.fillRect(0, 0, size.w, size.h)
g.brush = Color.green
particles.width.times |w|
{
particles.height.times |h|
{
if (particles.get(w, h)) // draw a 1x1 square for each set particle
g.fillRect (w, h, 1, 1)
}
}
}
} </lang>
Fortran
For RCImageBasic and RCImageIO, see Basic bitmap storage/Fortran and Write ppm file#Fortran
<lang fortran>program BrownianTree
use RCImageBasic use RCImageIO
implicit none
integer, parameter :: num_particles = 1000 integer, parameter :: wsize = 800
integer, dimension(wsize, wsize) :: world type(rgbimage) :: gworld integer :: x, y
! init seed call init_random_seed world = 0 call draw_brownian_tree(world)
call alloc_img(gworld, wsize, wsize)
call fill_img(gworld, rgb(0,0,0))
do y = 1, wsize
do x = 1, wsize
if ( world(x, y) /= 0 ) then
call put_pixel(gworld, x, y, rgb(255, 255, 255))
end if
end do
end do
open(unit=10, file='browniantree.ppm', action='write') call output_ppm(10, gworld) close(10)
call free_img(gworld)
contains
! this code is taken from the GNU gfortran online doc subroutine init_random_seed integer :: i, n, clock integer, dimension(:), allocatable :: seed
call random_seed(size = n) allocate(seed(n)) call system_clock(count = clock) seed = clock + 37 * (/ ( i - 1, i = 1, n) /) call random_seed(put = seed) deallocate(seed) end subroutine init_random_seed
function randbetween(a, b) result(res) ! suppose a < b integer, intent(in) :: a, b integer :: res
real :: r
call random_number(r)
res = a + int((b-a)*r + 0.5)
end function randbetween
function bounded(v, ll, ul) result(res) integer, intent(in) :: v, ll, ul logical res
res = ( v >= ll ) .and. ( v <= ul ) end function bounded
subroutine draw_brownian_tree(w) integer, dimension(:,:), intent(inout) :: w
integer :: px, py, dx, dy, i integer :: xsize, ysize
xsize = size(w, 1) ysize = size(w, 2)
w(randbetween(1, xsize), randbetween(1, ysize)) = 1
do i = 1, num_particles
px = randbetween(1, xsize)
py = randbetween(1, ysize)
do
dx = randbetween(-1, 1)
dy = randbetween(-1, 1)
if ( .not. bounded(dx+px, 1, xsize) .or. .not. bounded(dy+py, 1, ysize) ) then
px = randbetween(1, xsize)
py = randbetween(1, ysize)
else if ( w(px+dx, py+dy) /= 0 ) then
w(px, py) = 1
exit
else
py = py + dy
px = px + dx
end if
end do
end do
end subroutine draw_brownian_tree
end program</lang>
Go
The interpretation here of "collide" in the case of a new particle generated on top of a pixel of the existing tree is not to ignore the particle, but to find a place for it nearby. This properly increases the brightness of the area, reflecting that a particle was generated in the area. Visually, it appears to strengthen existing spines of the tree.
Using standard image library: <lang go>package main
import (
"fmt" "image" "image/color" "image/png" "math/rand" "os"
)
const w = 400 // image width const h = 300 // image height const n = 15000 // number of particles to add const frost = 255 // white
var g *image.Gray
func main() {
g = image.NewGray(image.Rectangle{image.Point{0, 0}, image.Point{w, h}})
// off center seed position makes pleasingly asymetrical tree
g.SetGray(w/3, h/3, color.Gray{frost})
generate:
for a := 0; a < n; {
// generate random position for new particle
rp := image.Point{rand.Intn(w), rand.Intn(h)}
if g.At(rp.X, rp.Y).(color.Gray).Y == frost {
// position is already set. find a nearby free position.
for {
rp.X += rand.Intn(3) - 1
rp.Y += rand.Intn(3) - 1
// execpt if we run out of bounds, consider the particle lost.
if !rp.In(g.Rect) {
continue generate
}
if g.At(rp.X, rp.Y).(color.Gray).Y != frost {
break
}
}
} else {
// else particle is in free space. let it wander
// until it touches tree
for !hasNeighbor(rp) {
rp.X += rand.Intn(3) - 1
rp.Y += rand.Intn(3) - 1
// but again, if it wanders out of bounds consider it lost.
if !rp.In(g.Rect) {
continue generate
}
}
}
// x, y now specify a free position toucing the tree.
g.SetGray(rp.X, rp.Y, color.Gray{frost})
a++
// progress indicator
if a%100 == 0 {
fmt.Println(a, "of", n)
}
}
f, err := os.Create("tree.png")
if err != nil {
fmt.Println(err)
return
}
err = png.Encode(f, g)
if err != nil {
fmt.Println(err)
}
f.Close()
}
var n8 = []image.Point{
{-1, -1}, {-1, 0}, {-1, 1},
{0, -1}, {0, 1},
{1, -1}, {1, 0}, {1, 1}}
func hasNeighbor(p image.Point) bool {
for _, n := range n8 {
o := p.Add(n)
if o.In(g.Rect) && g.At(o.X, o.Y).(color.Gray).Y == frost {
return true
}
}
return false
}</lang> Nearly the same, version below works with code from the bitmap task: <lang go>package main
// Files required to build supporting package raster are found in: // * Bitmap // * Grayscale image // * Write a PPM file
import (
"fmt" "math/rand" "raster"
)
const w = 400 // image width const h = 300 // image height const n = 15000 // number of particles to add const frost = 65535 // white
var g *raster.Grmap
func main() {
g = raster.NewGrmap(w, h) // off center seed position makes pleasingly asymetrical tree g.SetPx(w/3, h/3, frost) var x, y int
generate:
for a := 0; a < n; {
// generate random position for new particle
x, y = rand.Intn(w), rand.Intn(h)
switch p, ok := g.GetPx(x, y); p {
case frost:
// position is already set. find a nearby free position.
for p == frost {
x += rand.Intn(3) - 1
y += rand.Intn(3) - 1
p, ok = g.GetPx(x, y)
// execpt if we run out of bounds, consider the particle lost.
if !ok {
continue generate
}
}
default:
// else particle is in free space. let it wander
// until it touches tree
for !hasNeighbor(x, y) {
x += rand.Intn(3) - 1
y += rand.Intn(3) - 1
// but again, if it wanders out of bounds consider it lost.
_, ok = g.GetPx(x, y)
if !ok {
continue generate
}
}
}
// x, y now specify a free position toucing the tree.
g.SetPx(x, y, frost)
a++
// progress indicator
if a%100 == 0 {
fmt.Println(a, "of", n)
}
}
g.Bitmap().WritePpmFile("tree.ppm")
}
var n8 = [][]int{
{-1, -1}, {-1, 0}, {-1, 1},
{ 0, -1}, { 0, 1},
{ 1, -1}, { 1, 0}, { 1, 1}}
func hasNeighbor(x, y int) bool {
for _, n := range n8 {
if p, ok := g.GetPx(x+n[0], y+n[1]); ok && p == frost {
return true
}
}
return false
}</lang>
Haskell
The modules Bitmap, Bitmap.Netpbm, and Bitmap.BW are on Rosetta Code. The commented-out type signatures require scoped type variables in order to function.
<lang haskell>import Control.Monad import Control.Monad.ST import Data.STRef import Data.Array.ST import System.Random import Bitmap import Bitmap.BW import Bitmap.Netpbm
main = do
g <- getStdGen (t, _) <- stToIO $ drawTree (50, 50) (25, 25) 300 g writeNetpbm "/tmp/tree.pbm" t
drawTree :: (Int, Int) -> (Int, Int) -> Int -> StdGen -> ST s (Image s BW, StdGen) drawTree (width, height) start steps stdgen = do
img <- image width height off
setPix img (Pixel start) on
gen <- newSTRef stdgen
let -- randomElem :: [a] -> ST s a
randomElem l = do
stdgen <- readSTRef gen
let (i, stdgen') = randomR (0, length l - 1) stdgen
writeSTRef gen stdgen'
return $ l !! i
-- newPoint :: ST s (Int, Int)
newPoint = do
p <- randomElem border
c <- getPix img $ Pixel p
if c == off then return p else newPoint
-- wander :: (Int, Int) -> ST s ()
wander p = do
next <- randomElem $ filter (inRange pointRange) $ adjacent p
c <- getPix img $ Pixel next
if c == on then setPix img (Pixel p) on else wander next
replicateM_ steps $ newPoint >>= wander
stdgen <- readSTRef gen
return (img, stdgen)
where pointRange = ((0, 0), (width - 1, height - 1))
adjacent (x, y) = [(x - 1, y - 1), (x, y - 1), (x + 1, y - 1),
(x - 1, y), (x + 1, y),
(x - 1, y + 1), (x, y + 1), (x + 1, y + 1)]
border = liftM2 (,) [0, width - 1] [0 .. height - 1] ++
liftM2 (,) [1 .. width - 2] [0, height - 1]
off = black
on = white</lang>
Icon and Unicon
In this version the seed is randomly set within an inner area and particles are injected in an outer ring.
<lang Icon>link graphics,printf
procedure main() # brownian tree
Density := .08 # % particles to area SeedArea := .5 # central area to confine seed ParticleArea := .7 # central area to exclude particles appearing Height := Width := 400 # canvas
Particles := Height * Width * Density Field := list(Height) every !Field := list(Width)
Size := sprintf("size=%d,%d",Width,Height) Fg := sprintf("fg=%s",?["green","red","blue"]) Label := sprintf("label=Brownian Tree %dx%d PA=%d%% SA=%d%% D=%d%%",
Width,Height,ParticleArea*100,SeedArea*100,Density*100)
WOpen(Label,Size,Fg,"bg=black") | stop("Unable to open Window")
sx := Height * SetInside(SeedArea) sy := Width * SetInside(SeedArea) Field[sx,sy] := 1 DrawPoint(sx,sy) # Seed the field
Lost := 0
every 1 to Particles do {
repeat {
px := Height * SetOutside(ParticleArea)
py := Width * SetOutside(ParticleArea)
if /Field[px,py] then
break # don't materialize in the tree
}
repeat {
dx := delta()
dy := delta()
if not ( xy := Field[px+dx,py+dy] ) then {
Lost +:= 1
next # lost try again
}
if \xy then
break # collision
px +:= dx # move to clear spot
py +:= dy
}
Field[px,py] := 1
DrawPoint(px,py) # Stick the particle
}
printf("Brownian Tree Complete: Particles=%d Lost=%d.\n",Particles,Lost) WDone() end
procedure delta() #: return a random 1 pixel perturbation
return integer(?0 * 3) - 1
end
procedure SetInside(core) #: set coord inside area
return core * ?0 + (1-core)/2
end
procedure SetOutside(core) #: set coord outside area
pt := ?0 * (1 - core) pt +:= ( pt > (1-core)/2, core) return pt
end</lang>
graphics.icn provides graphics printf.icn provides printf
J
<lang j>brtr=:4 :0
seed=. ?x
clip=. 0 >. (<:x) <."1 ]
near=. [: clip +"1/&(,"0/~i:1)
p=.i.0 2
mask=. 1 (<"1 near seed)} x$0
field=.1 (<seed)} x$0
for.i.y do.
p=. clip (p +"1 <:?3$~$p),?x
b=.(<"1 p) { mask
fix=. b#p
if.#fix do. NB. if. works around j602 bug: 0(0#a:)}i.0 0
p=. (-.b)# p
mask=. 1 (<"1 near fix)} mask
field=. 1 (<"1 fix)} field
end.
end.
field
)</lang>
Example use:
<lang j> require'viewmat'
viewmat 480 640 brtr 30000</lang>
Note that building a brownian tree like this takes a while and would be more interesting if this were animated.
Java
<lang java>import java.awt.Graphics; import java.awt.image.BufferedImage; import java.util.*; import javax.swing.JFrame;
public class BrownianTree extends JFrame implements Runnable {
BufferedImage I; private List<Particle> particles; static Random rand = new Random();
public BrownianTree() {
super("Brownian Tree");
setBounds(100, 100, 400, 300);
setDefaultCloseOperation(EXIT_ON_CLOSE);
I = new BufferedImage(getWidth(), getHeight(), BufferedImage.TYPE_INT_RGB);
I.setRGB(I.getWidth() / 2, I.getHeight() / 2, 0xff00);
particles = new LinkedList<Particle>();
}
@Override
public void paint(Graphics g) {
g.drawImage(I, 0, 0, this);
}
public void run() {
for (int i = 0; i < 20000; i++) {
particles.add(new Particle());
}
while (!particles.isEmpty()) {
for (Iterator<Particle> it = particles.iterator(); it.hasNext();) {
if (it.next().move()) {
it.remove();
}
}
repaint();
}
}
public static void main(String[] args) {
BrownianTree b = new BrownianTree();
b.setVisible(true);
new Thread(b).start();
}
private class Particle {
private int x, y;
private Particle() {
x = rand.nextInt(I.getWidth());
y = rand.nextInt(I.getHeight());
}
/* returns true if either out of bounds or collided with tree */
private boolean move() {
int dx = rand.nextInt(3) - 1;
int dy = rand.nextInt(3) - 1;
if ((x + dx < 0) || (y + dy < 0)
|| (y + dy >= I.getHeight()) || (x + dx >= I.getWidth())) {
return true;
}
x += dx;
y += dy;
if ((I.getRGB(x, y) & 0xff00) == 0xff00) {
I.setRGB(x - dx, y - dy, 0xff00);
return true;
}
return false;
}
}
}</lang>
JavaScript + <canvas>
Live version <lang javascript>function brownian(canvasId, messageId) {
var canvas = document.getElementById(canvasId);
var ctx = canvas.getContext("2d");
// Options
var drawPos = true;
var seedResolution = 50;
var clearShade = 0; // 0..255
// Static state
var width = canvas.width;
var height = canvas.height;
var cx = width/2;
var cy = height/2;
var clearStyle = "rgba("+clearShade+", "+clearShade+", "+clearShade+", 1)";
// Utilities
function radius(x,y) {
return Math.sqrt((x-cx)*(x-cy)+(y-cx)*(y-cy));
}
function test(x, y) {
if (x < 0 || y < 0 || x >= width || y >= height)
return false;
var data = ctx.getImageData(x, y, 1, 1).data;
return data[0] != clearShade || data[1] != clearShade || data[2] != clearShade;
}
var shade = 120;
function setc(x, y, c) {
//var imgd = ctx.createImageData(1, 1);
//var pix = imgd.data;
//pix[0] = pix[1] = pix[2] = c == 255 ? 255 : shade;
//pix[3] = 255;
//shade = (shade + 1) % 254;
//ctx.putImageData(imgd, x, y);
//ctx.fillStyle = "rgba("+c+", "+c+", "+c+", 1)";
shade = (shade + 0.02) % 360;
if (c) {
ctx.fillStyle = "hsl("+shade+", 100%, 50%)";
} else {
ctx.fillStyle = clearStyle;
}
ctx.fillRect (x, y, 1, 1);
}
function set(x,y) {
setc(x,y,true);
}
function clear(x,y) {
setc(x,y,false);
}
// Initialize canvas to blank opaque ctx.fillStyle = clearStyle; ctx.fillRect (0, 0, width, height);
// Current position var x; var y;
// Farthest distance from center a particle has yet been placed. var closeRadius = 1;
// Place seed set(cx, cy);
// Choose a new random position for a particle (not necessarily unoccupied)
function newpos() {
// Wherever particles are injected, the tree will tend to grow faster
// toward it. Ideally, particles wander in from infinity; the best we
// could do is to have them wander in from the edge of the field.
// But in order to have the rendering occur in a reasonable time when
// the seed is small, without too much visible bias, we instead place
// the particles in a coarse grid. The final tree will cover every
// point on the grid.
//
// There's probably a better strategy than this.
x = Math.floor(Math.random()*(width/seedResolution))*seedResolution;
y = Math.floor(Math.random()*(height/seedResolution))*seedResolution;
}
newpos();
var animation;
animation = window.setInterval(function () {
if (drawPos) clear(x,y);
for (var i = 0; i < 10000; i++) {
var ox = x;
var oy = y;
// Changing this to use only the first four directions will result
// in a denser tree.
switch (Math.floor(Math.random()*8)) {
case 0: x++; break;
case 1: x--; break;
case 2: y++; break;
case 3: y--; break;
case 4: x++; y++; break;
case 5: x--; y++; break;
case 6: x++; y--; break;
case 7: x--; y--; break;
}
if (x < 0 || y < 0 ||
x >= width || y >= height ||
radius(x,y) > closeRadius+seedResolution+2) {
// wandered out of bounds or out of interesting range of the
// tree, so pick a new spot
var progress = 1000;
do {
newpos();
progress--;
} while ((test(x-1,y-1) || test(x,y-1) || test(x+1,y-1) ||
test(x-1,y ) || test(x,y ) || test(x+1,y ) ||
test(x-1,y+1) || test(x,y+1) || test(x+1,y+1)) && progress > 0);
if (progress <= 0) {
document.getElementById(messageId).appendChild(document.createTextNode("Stopped for lack of room."));
clearInterval(animation);
break;
}
}
if (test(x, y)) {
// hit something, mark where we came from and pick a new spot
set(ox,oy);
closeRadius = Math.max(closeRadius, radius(ox,oy));
newpos();
}
}
if (drawPos) set(x,y);
}, 1);
}</lang>
<lang html><html>
<head>
<script src="brownian.js"></script>
</head>
<body onload="brownian('canvas', 'message')">
<canvas id="canvas" width="402" height="402" style="border: 2px inset;"></canvas>
</body>
</html></lang>
Liberty BASIC
<lang lb>'[RC]Brownian motion tree
nomainwin dim screen(600,600) WindowWidth = 600 WindowHeight = 600 open "Brownian" for graphics_nsb_nf as #1 #1 "trapclose [quit]" #1 "down ; fill blue" rad=57.29577951 particles=500
'draw starting circle and mid point
for n= 1 to 360
x=300-(200*sin(n/rad))
y=300-(200*cos(n/rad))
#1, "color white ; set ";x;" ";y
screen(x,y)=1
next n
#1, "color white ; set 300 300"
screen(300,300)=1
'set up initial particles
dim particle(particles,9)'x y deltax deltay rotx roty
for n = 1 to particles
gosub [randomparticle]
next
'start timed drawing loop timer 17, [draw] wait
[draw]
#1 "discard"
scan
for n = 1 to particles
oldx=particle(n,1)
oldy=particle(n,2)
'erase particle
if not(screen(oldx,oldy)) then
#1 "color blue ; set ";oldx;" ";oldy
end if
'move particle x
particle(n,1)=particle(n,1)+int((sin(particle(n,6)/rad)*10)+particle(n,3))
particle(n,5)=particle(n,5)+6 mod 360
if particle(n,1)>599 or particle(n,1)<1 then gosub [randomparticle]
'move particle y
particle(n,2)=particle(n,2)+int((sin(particle(n,5)/rad)*10)+particle(n,4))
particle(n,6)=particle(n,6)+6 mod 360
if particle(n,2)>599 or particle(n,2)<1 then gosub [randomparticle]
'checkhit
x=particle(n,1)
y=particle(n,2)
if screen(x-1,y-1) or screen(x-1,y) or screen(x-1,y+1)_
or screen(x,y-1) or screen(x,y) or screen(x,y+1)_
or screen(x+1,y-1) or screen(x+1,y) or screen(x+1,y+1) then
#1 "color white ; set ";particle(n,1);" ";particle(n,2)
screen(particle(n,1),particle(n,2))=1
else
#1 "color red ; set ";particle(n,1);" ";particle(n,2)
end if
next
wait
[randomparticle] particle(n,1)=int(rnd(0)*599)+1 particle(n,2)=int(rnd(0)*599)+1 particle(n,3)=int(2-rnd(0)*4) particle(n,4)=int(2-rnd(0)*4) particle(n,5)=int(rnd(0)*360) particle(n,6)=int(rnd(0)*360) return
[quit] timer 0 close #1 end</lang>
Lua
The output is stored in as a ppm-image. The source code of these output-functions is located at Bitmap/Write a PPM file#Lua, Grayscale image#Lua, Basic bitmap storage#Lua. <lang lua>function SetSeed( f )
for i = 1, #f[1] do -- the whole boundary of the scene is used as the seed
f[1][i] = 1
f[#f][i] = 1
end
for i = 1, #f do
f[i][1] = 1
f[i][#f[1]] = 1
end
end
function SetParticle( f )
local pos_x, pos_y
repeat
pos_x = math.random( #f )
pos_y = math.random( #f[1] )
until f[pos_x][pos_y] == 0
return pos_x, pos_y
end
function Iterate( f, num_particles )
for i = 1, num_particles do
local pos_x, pos_y = SetParticle( f )
while true do
local dx = math.random(5) - 3
local dy = math.random(5) - 3
if ( pos_x+dx >= 1 and pos_x+dx <= #f and pos_y+dy >= 1 and pos_y+dy <= #f[1] ) then
if f[pos_x+dx][pos_y+dy] ~= 0 then
f[pos_x][pos_y] = 1
break
else
pos_x = pos_x + dx
pos_y = pos_y + dy
end
end
end
end
end
size_x, size_y = 400, 400 -- size of the scene
num_particles = 16000
math.randomseed( os.time() )
f = {} for i = 1, size_x do
f[i] = {}
for j = 1, size_y do
f[i][j] = 0
end
end
SetSeed( f ) Iterate( f, num_particles )
-- prepare the data for writing into a ppm-image file for i = 1, size_x do
for j = 1, size_y do
if f[i][j] == 1 then f[i][j] = 255 end
end
end Write_PPM( "brownian_tree.ppm", ConvertToColorImage(f) )</lang>
Mathematica
There is a prettier version at the Mathematica demo site. Its source code is also available there but it is not mine.
Loose
<lang Mathematica>canvasdim = 1000; n = 0.35*canvasdim^2; canvas = ConstantArray[0, {canvasdim, canvasdim}]; init = Floor@(0.5*{canvasdim, canvasdim}); (*RandomInteger[canvasdim,2]*) canvas[[init1, init2]] = 1; (*1st particle initialized to midpoint*)
Monitor[ (*Provides real-time intermediate result monitoring*)
Do[
particle = RandomInteger[canvasdim, 2];
While[True,
ds = RandomInteger[{-1, 1}, 2];
While[ (*New Particle Domain Limit Section*)
!And @@ (0 < (particle + ds)# <= canvasdim & /@ {1, 2}),
particle = RandomInteger[canvasdim, 2];
];
(* Particle Aggregation Section *)
If[canvas[[(particle + ds)1, (particle + ds)2]] > 0,
canvas[[particle1, particle2]] = i;
Break[],
particle += ds
];
],
{i, n}],
{i, (particle + ds), MatrixPlot@canvas}
]
MatrixPlot[canvas,FrameTicks->None,ColorFunction->"DarkRainbow",ColorRules->{0 -> None}]</lang>
Result:
OCaml
<lang ocaml>let world_width = 400 let world_height = 400 let num_particles = 20_000
let () =
assert(num_particles > 0); assert(world_width * world_height > num_particles);
let dla ~world =
(* put the tree seed *)
world.(world_height / 2).(world_width / 2) <- 1;
for i = 1 to num_particles do
(* looping helper function *)
let rec aux px py =
(* randomly choose a direction *)
let dx = (Random.int 3) - 1 (* offsets *)
and dy = (Random.int 3) - 1 in
if dx + px < 0 || dx + px >= world_width ||
dy + py < 0 || dy + py >= world_height then
(* plop the particle into some other random location *)
aux (Random.int world_width) (Random.int world_height)
else if world.(py + dy).(px + dx) <> 0 then
(* bumped into something, particle set *)
world.(py).(px) <- 1
else
aux (px + dx) (py + dy)
in
(* set particle's initial position *)
aux (Random.int world_width) (Random.int world_height)
done
let to_pbm ~world =
print_endline "P1"; (* Type=Portable bitmap, Encoding=ASCII *) Printf.printf "%d %d\n" world_width world_height; Array.iter (fun line -> Array.iter print_int line; print_newline() ) world
let () =
Random.self_init(); let world = Array.make_matrix world_width world_height 0 in dla ~world; to_pbm ~world;
- </lang>
better to compile to native code to get a faster program:
$ ocamlopt -o brownian_tree.opt brownian_tree.ml $ ./brownian_tree.opt | display -
Octave
<lang octave>function r = browniantree(xsize, ysize = xsize, numparticle = 1000)
r = zeros(xsize, ysize, "uint8");
r(unidrnd(xsize), unidrnd(ysize)) = 1;
for i = 1:numparticle
px = unidrnd(xsize-1)+1;
py = unidrnd(ysize-1)+1;
while(1)
dx = unidrnd(2) - 1;
dy = unidrnd(2) - 1;
if ( (dx+px < 1) || (dx+px > xsize) || (dy+py < 1) || (dy+py > ysize) )
px = unidrnd(xsize-1)+1; py = unidrnd(ysize-1)+1;
elseif ( r(px+dx, py+dy) != 0 )
r(px, py) = 1; break;
else
px += dx; py += dy;
endif endwhile endfor
endfunction
r = browniantree(200); r( r > 0 ) = 255; jpgwrite("browniantree.jpg", r, 100); % image package</lang>
Perl
Simulation code. Tremendously slow, partly because it doesn't use a grid-based collision checking. Showing three sample images with different STEP and ATTRACT parameters, to demonstrate how sensitive the result is to them.
Code runs until the tree reached specified radius. Output is written to "test.eps" of wherever the current directory is. The 0-0 sample took maybe 3 hours (I don't really know, I went for dinner.) <lang perl>sub PI() { atan2(1,1) * 4 } # The, er, pi sub STEP() { .5 } # How far does the particle move each step. Affects
# both speed and accuracy greatly
sub STOP_RADIUS() { 100 } # When the tree reaches this far from center, end
- At each step, move this much towards center. Bigger numbers help the speed because
- particles are less likely to wander off, but greatly affects tree shape.
- Should be between 0 and 1 ish. Set to 0 for pain.
sub ATTRACT() { .2 }
my @particles = map([ map([], 0 .. 2 * STOP_RADIUS) ], 0 .. 2 * STOP_RADIUS); push @{ $particles[STOP_RADIUS][STOP_RADIUS] }, [0, 0];
my $r_start = 3; my $max_dist = 0;
sub dist2 {
my ($dx, $dy) = ($_[0][0] - $_[1][0], $_[0][1] - $_[1][1]);
$dx * $dx + $dy * $dy
}
sub move {
my $p = shift;
# moved too far, kill particle
# return if dist2($p, [0, 0]) > 2 * $r_start * $r_start;
$p->[0] += 2 * $r_start while $p->[0] < -$r_start;
$p->[0] -= 2 * $r_start while $p->[0] > $r_start;
$p->[1] += 2 * $r_start while $p->[1] < -$r_start;
$p->[1] -= 2 * $r_start while $p->[1] > $r_start;
my ($ix, $iy) = (int($p->[0]), int($p->[1]));
my $dist = 2 * $r_start * $r_start;
my $nearest;
# see if the particle is close enough to stick to an exist one
for ($ix - 1 .. $ix + 1) {
my $idx = STOP_RADIUS + $_;
next if $idx > 2 * STOP_RADIUS || $idx < 0;
my $xs = $particles[ $idx ];
for ($iy - 1 .. $iy + 1) {
my $idx = STOP_RADIUS + $_;
next if $idx > 2 * STOP_RADIUS || $idx < 0;
for (@{ $xs->[ $idx ] }) {
my $d = dist2($p, $_);
next if $d > 2;
next if $d > $dist;
$dist = $d;
$nearest = $_;
}
}
}
# yes, found one
if ($nearest) {
my $displace = [ $p->[0] - $nearest->[0],
$p->[1] - $nearest->[1] ];
my $angle = atan2($displace->[1], $displace->[0]);
$p->[0] = $nearest->[0] + cos($angle);
$p->[1] = $nearest->[1] + sin($angle);
push @{$particles[$ix + STOP_RADIUS][$iy + STOP_RADIUS]}, [ @$p ];
$dist = sqrt dist2($p);
if ($dist + 10 > $r_start && $r_start < STOP_RADIUS + 10) {
$r_start = $dist + 10
}
if (int($dist + 1) > $max_dist) {
$max_dist = int($dist + 1);
# write_eps();
# system('pstopnm -portrait -xborder 0 -yborder 0 test.eps 2> /dev/null');
# system('pnmtopng test.eps001.ppm 2>/dev/null > test.png');
return 3 if $max_dist >= STOP_RADIUS;
}
return 2;
}
# random walk
my $angle = rand(2 * PI);
$p->[0] += STEP * cos($angle);
$p->[1] += STEP * sin($angle);
# drag particle towards center by some distance
my $nudge;
if (sqrt(dist2($p, [0, 0])) > STOP_RADIUS + 1) {
$nudge = 1;
} else {
$nudge = STEP * ATTRACT;
}
if ($nudge) {
$angle = atan2($p->[1], $p->[0]);
$p->[0] -= $nudge * cos($angle);
$p->[1] -= $nudge * sin($angle);
}
return 1;
}
my $count; PARTICLE: while (1) {
my $a = rand(2 * PI);
my $p = [ $r_start * cos($a), $r_start * sin($a) ];
while ($_ = move($p)) {
given ($_) {
when (1) { next }
when (2) { $count++; last; }
when (3) { last PARTICLE }
default { last }
}
}
print STDERR "$count $max_dist/@{[int($r_start)]}/@{[STOP_RADIUS]}\r" unless $count% 7;
}
sub write_eps {
my $size = 128;
my $p = $size / (STOP_RADIUS * 1.05);
my $b = STOP_RADIUS * $p;
if ($p < 1) {
$size = STOP_RADIUS * 1.05;
$b = STOP_RADIUS;
$p = 1;
}
my $hp = $p / 2;
open OUT, ">", "test.eps";
# print EPS to standard out
print OUT <<"HEAD";
%!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 0 0 @{[$size*2, $size*2]} $size $size translate /l{ rlineto }def /c{ $hp 0 360 arc fill }def -$size -$size moveto $size 2 mul 0 l 0 $size 2 mul l -$size 2 mul 0 l closepath 0 setgray fill 0 setlinewidth .1 setgray 0 0 $b 0 360 arc stroke .8 setgray /TimesRoman findfont 16 scalefont setfont -$size 10 add $size -16 add moveto (Step = @{[STEP]} Attract = @{[ATTRACT]}) show 0 1 0 setrgbcolor newpath HEAD
for (@particles) {
for (@$_) {
printf OUT "%.3g %.3g c ", map { $_ * $p } @$_ for @$_;
}
}
print OUT "\n%%EOF";
close OUT;
}
write_eps;</lang>
PicoLisp
<lang PicoLisp>(load "@lib/simul.l")
(de brownianTree (File Size Cnt)
(let Img (grid Size Size)
(put Img (/ Size 2) (/ Size 2) 'pix T)
(use (P Q)
(do Cnt
(setq P (get Img (rand 1 Size) (rand 1 Size)))
(loop
(setq Q ((if2 (rand T) (rand T) north east south west) P))
(T (; Q pix) (put P 'pix T))
(setq P (or Q (get Img (rand 1 Size) (rand 1 Size)))) ) ) )
(out "img.pbm"
(prinl "P1")
(prinl Size " " Size)
(for L Img
(for This L
(prin (if (: pix) 1 0)) )
(prinl) ) ) ) )</lang>
Use:
(brownianTree "img.pbm" 300 9000) (call 'display "img.pbm")
PureBasic
<lang PureBasic>#Window1 = 0
- Image1 = 0
- ImgGadget = 0
- NUM_PARTICLES = 3000
- width = 200
- height = 200
- xmax = #width -3
- ymax = #height -3
Define.i Event ,i ,x,y
If OpenWindow(#Window1, 0, 0, #width, #height, "Brownian Tree PureBasic Example", #PB_Window_SystemMenu )
If CreateImage(#Image1, #width, #height)
ImageGadget(#ImgGadget, 0, 0, #width, #height, ImageID(#Image1))
StartDrawing(ImageOutput(#Image1))
FrontColor($FFFFFF)
Plot( Random(#xmax) , Random(#ymax ))
StopDrawing()
SetGadgetState(#ImgGadget, ImageID(#Image1))
For i = 1 To #NUM_PARTICLES
x = Random(#xmax)+1 : y = Random (#ymax)+1
StartDrawing(ImageOutput(#Image1))
While Point(x+1, y+1) + Point(x, y+1)+Point(x+1, y)+Point(x-1, y-1)+Point(x-1, y)+Point(x, y-1) = 0
x = x + (Random(2)-1) : y = y + (Random(2)-1)
If x < 1 Or x > #xmax Or y < 1 Or y > #ymax
x = Random(#xmax)+1 : y = Random (#ymax)+1
EndIf
Wend
Plot(x,y)
StopDrawing()
SetGadgetState(#ImgGadget, ImageID(#Image1))
Next
EndIf
Repeat
Event = WaitWindowEvent()
Until Event = #PB_Event_CloseWindow
EndIf</lang>
Python
<lang python>import pygame, sys, os from pygame.locals import * from random import randint pygame.init()
MAXSPEED = 15 SIZE = 3 COLOR = (45, 90, 45) WINDOWSIZE = 400 TIMETICK = 1 MAXPART = 50
freeParticles = pygame.sprite.Group() tree = pygame.sprite.Group()
window = pygame.display.set_mode((WINDOWSIZE, WINDOWSIZE)) pygame.display.set_caption("Brownian Tree")
screen = pygame.display.get_surface()
class Particle(pygame.sprite.Sprite):
def __init__(self, vector, location, surface):
pygame.sprite.Sprite.__init__(self)
self.vector = vector
self.surface = surface
self.accelerate(vector)
self.add(freeParticles)
self.rect = pygame.Rect(location[0], location[1], SIZE, SIZE)
self.surface.fill(COLOR, self.rect)
def onEdge(self):
if self.rect.left <= 0:
self.vector = (abs(self.vector[0]), self.vector[1])
elif self.rect.top <= 0:
self.vector = (self.vector[0], abs(self.vector[1]))
elif self.rect.right >= WINDOWSIZE:
self.vector = (-abs(self.vector[0]), self.vector[1])
elif self.rect.bottom >= WINDOWSIZE:
self.vector = (self.vector[0], -abs(self.vector[1]))
def update(self):
if freeParticles in self.groups():
self.surface.fill((0,0,0), self.rect)
self.remove(freeParticles)
if pygame.sprite.spritecollideany(self, freeParticles):
self.accelerate((randint(-MAXSPEED, MAXSPEED),
randint(-MAXSPEED, MAXSPEED)))
self.add(freeParticles)
elif pygame.sprite.spritecollideany(self, tree):
self.stop()
else:
self.add(freeParticles)
self.onEdge()
if (self.vector == (0,0)) and tree not in self.groups():
self.accelerate((randint(-MAXSPEED, MAXSPEED),
randint(-MAXSPEED, MAXSPEED)))
self.rect.move_ip(self.vector[0], self.vector[1])
self.surface.fill(COLOR, self.rect)
def stop(self):
self.vector = (0,0)
self.remove(freeParticles)
self.add(tree)
def accelerate(self, vector):
self.vector = vector
NEW = USEREVENT + 1 TICK = USEREVENT + 2
pygame.time.set_timer(NEW, 50) pygame.time.set_timer(TICK, TIMETICK)
def input(events):
for event in events:
if event.type == QUIT:
sys.exit(0)
elif event.type == NEW and (len(freeParticles) < MAXPART):
Particle((randint(-MAXSPEED,MAXSPEED),
randint(-MAXSPEED,MAXSPEED)),
(randint(0, WINDOWSIZE), randint(0, WINDOWSIZE)),
screen)
elif event.type == TICK:
freeParticles.update()
half = WINDOWSIZE/2
tenth = WINDOWSIZE/10
root = Particle((0,0),
(randint(half-tenth, half+tenth),
randint(half-tenth, half+tenth)), screen)
root.stop()
while True:
input(pygame.event.get()) pygame.display.flip()</lang>
REXX
A large part of the REXX program's prologue was to handle the various options.
With a little more REXX code, a petri dish option could be added, that is, when a particle hits the
edge, it "bounces" back. Also, the field could then be displayed as a round area (a petri dish).
REXX code was added to do snapshots of the field, either after so many cycles, and/or after some elapsed
time has elasped (whole seconds only). This makes for some facinating observations.
<lang rexx>/*REXX program shows brownian motion of dust in a field with one seed. */
parse arg height width motes .
if height== | height==',' then height=0
if width== | width==',' then width=0
if motes== then motes='10%' /*nn% Calculate # of dust motes.*/
/* ... otherwise just the number.*/
tree ='*' /*an affixed dust speck (tree). */ mote ='fa'x /*char for a loose mote (of dust)*/ empty=' ' /*char for an empty spot in field*/ clearScr='CLS' /*(DOS?) command to clear screen.*/ eons=1000000 /*time limit for browian movement*/ snapshot=0 /*every n winks, show snapshot.*/ snaptime=2 /*every n secs, show snapshot.*/ seedPos=30 45 /*place seed in this field pos. */ seedPos=0 /*if =0, use middle of the field.*/
/*if -1, use random placement. */
/*otherwise, place it at seedPos.*/
randseed=0 /*set RANDSEED for repeatability.*/ if randseed\==0 then call random ,,randseed /*set the 1st random num.*/
if height==0 | width==0 then _=scrsize() /*not all REXXes have SCRSIZE.*/ if height==0 then height=word(_,1)-3 if width==0 then width=word(_,2)-1
seedAt=seedPos
if seedPos== 0 then seedAt=width%2 height%2 if seedPos==-1 then seedAt=random(1,width) random(1,height) parse var seedAt xs ys .
if right(motes,1)=='%' then motes=height*width*strip(motes,,'%')%100 @.=empty /*create the field, all empty. */
do j=1 for motes /*sprinkle dust motes randomly. */
rx=random(1, width); ry=random(1,height); @.rx.ry=mote
end
/*plant the seed from which the */
/*tree will grow from dust motes */
@.xs.ys=tree /*that affixed themselves. */ call show /*show field before we mess it up*/ tim=0 /*the time (in secs) of last show*/ loX=1; hiX= width /*used to optimize mote searching*/ loY=1; hiY=height /* " " " " " */
/*─────────────────────────────soooo, this is brownian motion.*/
do winks=1 for eons until \motion /*EONs is used just in case of ∞.*/
motion=0 /*turn off brownian motion flag. */
if snapshot\==0 then if winks//snapshot==0 then call show
if snaptime\==0 then do; t=time('S')
if t\==tim & t//snaptime==0 then do
call show
tim=time('s')
end
end
minX=loX; maxX=hiX /*as the tree grows, the search */ minY=loY; maxY=hiY /* for dust motes gets faster. */ loX= width; hiX=1 /*used to limit mote searching. */ loY=height; hiY=1 /* " " " " " */
do x=minX to maxX; xm=x-1; xp=x+1
do y=minY to maxY; if @.x.y\==mote then iterate
if x<loX then loX=x; if x>hiX then hiX=x /*is faster than: hiX=max(X hiX) */
if y<loY then loY=y; if y>hiY then hiY=y /*is faster than: hiY=max(y hiY) */
if @.xm.y ==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
if @.xp.y ==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
ym=y-1
if @.x.ym ==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
if @.xm.ym==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
if @.xp.ym==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
yp=y+1
if @.x.yp ==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
if @.xm.yp==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
if @.xp.yp==tree then do; @.x.y=tree; iterate; end /*neighbor?*/
motion=1 /*brownian motion is coming up. */
xb=x+random(1,3)-2 /*apply brownian motion for X. */
yb=y+random(1,3)-2 /*apply brownian motion for Y. */
if @.xb.yb\==empty then iterate /*can the mote move there ? */
@.x.y=empty /*"blank" out the old position. */
@.xb.yb=mote /*move the mote (or possibly not)*/
if xb<loX then loX=max(1,xb); if xb>hiX then hiX=min( width,xb)
if yb<loY then loY=max(1,yb); if yb>hiY then hiY=min(height,yb)
end /*y*/
end /*x*/
call crop
end /*winks*/
call show exit /*────────────────────────────────SHOW subroutine───────────────────────*/ show: clearScr /*not necessary, but speeds it up*/
do ys=height by -1 for height; aRow=
do xs=1 for width; aRow=aRow||@.xs.ys
end /*xs*/
say aRow
end /*ys*/
return /*────────────────────────────────CROP subroutine───────────────────────*/ crop: if loX>1 & hiX<width & loY>1 & hiY<height then return /*cropping?*/
do yc=-1 to height+1 by height+2 /*delete motes (moved off field).*/
do xc=-1 to width+1; if @.xc.yc==empty then iterate; @.xc.yc=empty
end /*xc*/
end /*yc*/
do xc=-1 to width+1 by width+2 /*delete motes (moved off field).*/
do yc=-1 to height+1; if @.xc.yc==empty then iterate; @.xc.yc=empty
end /*yc*/
end /*xc*/
return</lang> output when using the default input
* *
**
* *
* * * ****
*** * * * * *
* * * * * * **
** ** * ** *
* ** * * **
** * ** * *
** * ** * * * *
* * * * **
* * ** ** * * *** *
* * * * *
* * * * * * * * *
** * ** * * ** * **
* * * * * * ** * *
* ** * * ** * * *
* * * ** * ** *
* * * * * * *
* * * * ** * * *
* *** * * * * ** * **
* *** * ** * ** * * ** ** * *
** * * * * ** * * * *
* * * * * ** * * *** *
** ** * * * * * * ** ** * * * * **
* * * * ** * * * * ** ** * * *
* * * * * * * * *
* * ** * ** * * * **
* * *** * **** * * * * *
* **** * * * * * **** * ** *
* * * * * *** * * ** ** **
* * * * * * ** * * * * *** * ***
** * * * ** * * * ** * ** ** *
** * * * * * ** ** * * * **
* * * * * * * * ** ** * ** **
* * * ** * * * * * * * * **** *
* * * * * ** * ** * * *** * * * * **
** ** ** * ** ** * * * * * ** *
* * * ** * * * * * * *
* * ** * * * * ** * * * * * * *
* * * * * ** * * * * * ** * * *
* ** * * * * * *** * * ** **
* * * * * * * * ** * * * * * ** *
* * * * ** * ** * * * * * ** * * *
*** * * * * * * * * * * * * * * * *
* * * ** * * * * * * ** * * * * * * * *** * *** * * ** * * *
** * * * * * ** * ** ** ** * * ** * * *** * ** * * * * ** * *
* * * * * * * * * * * * * * * ** * * * ** * ** *
* * * * * ** ** ****** * * ** * ** * * ** * * * * * * * ** * * * ** *
* * ** * ** * * * ** ** ** * ** ** * * * * * * * * * * ** * ** *
** * * * * * * * * * * * * * * * * ** * * * * * * * *
* *** * * * * * * * * ** ** * * * * * * * *** * * * *** *
* * * * * * * * * * * * ** * * * ** * * * ** * * ** * * *
** * ** * * * ** ** * * * * ** * ** * * * * *
* * * * * * ** ***** * * ** * * * ** * *
* * * ** * * ** * * * * * * ** * * ** * ** * ** *
* * * * * * * * * * * * * * * * * * ** *
* * * ** * * * * ** * * **** ** * * *
** * * ** * ** * * * * * * * * ** ** * * *
* ** * * * * * * ** * * * * * * * * * *
* * * ***** *** ** * * ** * ** * *** * ** * * ** ** *
** * * * * * ** * * ** * * * * *
* * * * * * * * * * * * * * * * *
* ** *** * * * * * * ** * * * ***
* * * * * * ** * * * *
** * * * * * * * * * * *
* ** * ** * ** * ** * * * * * *
* ** * * * * * ** * * * * *
* * * * ** * * * * * * * * *
* * * * * ** ** * * * * *
* * * ** * * * * * * *
** *** * * * ** * *
*** * * * * * ** ** * * **
* * *** * * * * **
* * * * * *
** *
* * *
* *
* ***
* * *
* * **
* * *
*
Ruby
<lang ruby>require 'rubygems' require 'RMagick'
NUM_PARTICLES = 1000 SIZE = 800
def draw_brownian_tree world
# set the seed world[rand SIZE][rand SIZE] = 1
NUM_PARTICLES.times do # set particle's position px = rand SIZE py = rand SIZE
loop do
# randomly choose a direction
dx = rand(3) - 1
dy = rand(3) - 1
if dx + px < 0 or dx + px >= SIZE or dy + py < 0 or dy + py >= SIZE
# plop the particle into some other random location
px = rand SIZE
py = rand SIZE
elsif world[py + dy][px + dx] != 0
# bumped into something
world[py][px] = 1
break
else
py += dy
px += dx
end
end
end
end
world = Array.new(SIZE) { Array.new(SIZE, 0) } srand Time.now.to_i
draw_brownian_tree world
img = Magick::Image.new(SIZE, SIZE) do
self.background_color = "black"
end
draw = Magick::Draw.new draw.fill "white"
world.each_with_index do |row, y|
row.each_with_index do |colour, x| draw.point x, y if colour != 0 end
end
draw.draw img img.write "brownian_tree.bmp"</lang>
Run BASIC
<lang runbasic>numParticles = 3000 dim canvas(201,201) canvas(rnd(1) * 100 , rnd(1) * 200) = 1 'start point for i = 1 To numParticles
x = (rnd(1) * 199) + 1 y = (rnd(1) * 199) + 1
while canvas(x+1, y+1) + canvas(x, y+1)+canvas(x+1, y)+canvas(x-1, y-1)+canvas(x-1, y)+canvas(x, y-1) = 0
x = x + (rnd(1)* 2) + 1
y = y + (rnd(1)* 2) + 1
If x < 1 Or x > 200 Or y < 1 Or y > 200 then
x = (rnd(1) * 199) + 1
y = (rnd(1) * 199) + 1
end if
wend
canvas(x,y) = 1
next i
graphic #g, 200,200 for x = 1 to 200
for y = 1 to 200
if canvas(x,y) = 1 then #g "color green ; set "; x; " "; y else #g "color blue ; set "; x; " "; y
next y
next x render #g
- g "flush"</lang>
Scheme
<lang scheme>; Save bitmap to external file (define (save-pbm bitmap filename) (define f (open-output-file filename)) (simple-format f "P1\n~A ~A\n" (list-ref (array-dimensions bitmap) 0) (list-ref (array-dimensions bitmap) 1)) (do ((c 0 (+ c 1))) ((eqv? c (list-ref (array-dimensions bitmap) 1))) (do ((r 0 (+ r 1))) ((eqv? r (list-ref (array-dimensions bitmap) 0))) (display (array-ref bitmap r c) f)) (newline f)) (close-output-port f) )
- Return a random coordinate in the bitmap that isn't filled yet along with a direction
(define (new-particle bitmap) (define x (random (list-ref (array-dimensions bitmap) 0))) (define y (random (list-ref (array-dimensions bitmap) 1))) (define dx (- (random 3) 1)) (define dy (- (random 3) 1)) ;Repeat until we find an unused location (if (> (array-ref bitmap x y) 0) (new-particle bitmap) (list (list x y) (list dx dy))))
- Check neighboring coordinates to see if a collision occured
(define (collision-check bitmap p) (define c #f) (define oob #f) (define x (list-ref (car p) 0)) (define y (list-ref (car p) 1)) (define dx (list-ref (cadr p) 0)) (define dy (list-ref (cadr p) 1)) (define w (list-ref (array-dimensions bitmap) 0)) (define h (list-ref (array-dimensions bitmap) 1))
; If the particle hasn't gone out of bounds keep checking for a collision (if (or (> 0 x) (> 0 y) (<= w x) (<= h y)) (set! oob #t) (do ((x (- (list-ref (car p) 0) 1) (+ x 1))) ((eqv? x (+ (list-ref (car p) 0) 2))) (do ((y (- (list-ref (car p) 1) 1) (+ y 1))) ((eqv? y (+ (list-ref (car p) 1) 2))) ; Check existing neighbors for collisions (if (and (<= 0 x) (<= 0 y) (> w x) (> h y)) (if (not (zero? (array-ref bitmap x y))) (set! c #t)))))) (if oob #f ; Return false if out of bounds (if c p ; Return the point of collision if a collision occured (if (and (zero? dx) (zero? dy)) #f ; Return false if particle is motionless with no collision (collision-check bitmap (particle-move p))))))
- Plot a particle on the bitmap
(define (particle-plot! bitmap p) (array-set! bitmap 1 (list-ref (car p) 0) (list-ref (car p) 1)))
- Move a particle along its slope
(define (particle-move p) (list (list (+ (list-ref (car p) 0) (list-ref (cadr p) 0)) (+ (list-ref (car p) 1) (list-ref (cadr p) 1))) (cadr p)))
- Grow a brownian tree
(define (grow-brownian-tree! bitmap collisions) (define w (list-ref (array-dimensions bitmap) 0)) (define h (list-ref (array-dimensions bitmap) 1))
; Generate a new particle at a random location (define p (new-particle bitmap))
; Find a collision or lack of one and plot it on the bitmap (set! p (collision-check bitmap p)) (if p (begin ; Display collision number and the place it happened (display collisions)(display ": ")(display (car p))(newline) (set! collisions (- collisions 1)) ; Plot the point (particle-plot! bitmap p)))
; If we're done say so (if (zero? collisions) (display "Done\n"))
; Keep going until we have enough collisions ; or have filled the bitmap (if (and (< 0 collisions) (memq 0 (array->list (array-contents bitmap)))) (grow-brownian-tree! bitmap collisions)))
- Plot a random point to seed the brownian tree
(define (seed-brownian-tree! bitmap) (define p (new-particle bitmap)) (particle-plot! bitmap p))
- Example usage ;;;
- Seed the random number generator
(let ((time (gettimeofday))) (set! *random-state* (seed->random-state (+ (car time) (cdr time)))))
- Generate a tree with 320*240 collisions on a bitmap of the size 640x480
- The bitmap is zeroed to start and written with a one where a collision occurs
(define bitmap (make-array 0 640 480)) (seed-brownian-tree! bitmap) (grow-brownian-tree! bitmap (* 320 240))
- Save to a portable bitmap file
(save-pbm bitmap "brownian-tree.pbm")</lang>
Seed7
The program below generates a small brownian tree. You can watch how it grows.
<lang seed7>$ include "seed7_05.s7i";
include "draw.s7i"; include "keybd.s7i";
const integer: SIZE is 300; const integer: SCALE is 1;
const proc: genBrownianTree (in integer: fieldSize, in integer: numParticles) is func
local
var array array integer: world is 0 times 0 times 0;
var integer: px is 0;
var integer: py is 0;
var integer: dx is 0;
var integer: dy is 0;
var integer: i is 0;
var boolean: bumped is FALSE;
begin
world := fieldSize times fieldSize times 0;
world[rand(1, fieldSize)][rand(1, fieldSize)] := 1; # Set the seed
for i range 1 to numParticles do
# Set particle's initial position
px := rand(1, fieldSize);
py := rand(1, fieldSize);
bumped := FALSE;
repeat
# Randomly choose a direction
dx := rand(-1, 1);
dy := rand(-1, 1);
if dx + px < 1 or dx + px > fieldSize or dy + py < 1 or dy + py > fieldSize then
# Plop the particle into some other random location
px := rand(1, fieldSize);
py := rand(1, fieldSize);
elsif world[py + dy][px + dx] <> 0 then
# Bumped into something
world[py][px] := 1;
rect(SCALE * pred(px), SCALE * pred(py), SCALE, SCALE, white);
DRAW_FLUSH;
bumped := TRUE;
else
py +:= dy;
px +:= dx;
end if;
until bumped;
end for;
end func;
const proc: main is func
begin screen(SIZE * SCALE, SIZE * SCALE); KEYBOARD := GRAPH_KEYBOARD; genBrownianTree(SIZE, 20000); readln(KEYBOARD); end func;</lang>
Original source: [1]
Tcl
<lang tcl>package require Tcl 8.5 package require Tk
set SIZE 300
image create photo brownianTree -width $SIZE -height $SIZE interp alias {} plot {} brownianTree put white -to brownianTree put black -to 0 0 [expr {$SIZE-1}] [expr {$SIZE-1}] proc rnd {range} {expr {int(rand() * $range)}}
proc makeBrownianTree count {
global SIZE
# Set the seed
plot [rnd $SIZE] [rnd $SIZE]
for {set i 0} {$i<$count} {incr i} {
# Set a random particle's initial position set px [rnd $SIZE] set py [rnd $SIZE]
while 1 { # Randomly choose a direction set dx [expr {[rnd 3] - 1}] set dy [expr {[rnd 3] - 1}]
# If we are going out of bounds... if {$px+$dx < 0 || $px+$dx >= $SIZE || $py+$dy < 0 || $py+$dy>=$SIZE} { # Out of bounds, so move back in set dx [expr {[rnd 3] - 1}] set dy [expr {[rnd 3] - 1}] continue }
set ox $px set oy $py # Move/see if we would hit anything incr px $dx incr py $dy if {[lindex [brownianTree get $px $py] 0]} { # Hit something, so plot where we were plot $ox $oy break } } ## For display while things are processing, uncomment next line #update;puts -nonewline .;flush stdout
}
}
pack [label .l -image brownianTree] update makeBrownianTree 1000 brownianTree write tree.ppm</lang>
Visual Basic .NET
Windows Forms Application.
<lang vbnet> Imports System.Drawing.Imaging
Public Class Form1
ReadOnly iCanvasColor As Integer = Color.Black.ToArgb ReadOnly iSeedColor As Integer = Color.White.ToArgb
Dim iCanvasWidth As Integer = 0 Dim iCanvasHeight As Integer = 0
Dim iPixels() As Integer = Nothing
Private Sub BrownianTree()
Dim oCanvas As Bitmap = Nothing Dim oRandom As New Random(Now.Millisecond) Dim oXY As Point = Nothing Dim iParticleCount As Integer = 0
iCanvasWidth = ClientSize.Width iCanvasHeight = ClientSize.Height
oCanvas = New Bitmap(iCanvasWidth, iCanvasHeight, Imaging.PixelFormat.Format24bppRgb)
Graphics.FromImage(oCanvas).Clear(Color.FromArgb(iCanvasColor))
iPixels = GetData(oCanvas)
' We'll use about 10% of the total number of pixels in the canvas for the particle count. iParticleCount = CInt(iPixels.Length * 0.1)
' Set the seed to a random location on the canvas. iPixels(oRandom.Next(iPixels.Length)) = iSeedColor
' Run through the particles.
For i As Integer = 0 To iParticleCount
Do
' Find an open pixel.
oXY = New Point(oRandom.Next(oCanvas.Width), oRandom.Next(oCanvas.Height))
Loop While iPixels(oXY.Y * oCanvas.Width + oXY.X) = iSeedColor
' Jitter until the pixel bumps another.
While Not CheckAdjacency(oXY)
oXY.X += oRandom.Next(-1, 2)
oXY.Y += oRandom.Next(-1, 2)
' Make sure we don't jitter ourselves out of bounds.
If oXY.X < 0 Then oXY.X = 0 Else If oXY.X >= oCanvas.Width Then oXY.X = oCanvas.Width - 1
If oXY.Y < 0 Then oXY.Y = 0 Else If oXY.Y >= oCanvas.Height Then oXY.Y = oCanvas.Height - 1
End While
iPixels(oXY.Y * oCanvas.Width + oXY.X) = iSeedColor
' If you'd like to see updates as each particle collides and becomes
' part of the tree, uncomment the next 4 lines (it does slow it down slightly).
' SetData(oCanvas, iPixels)
' BackgroundImage = oCanvas
' Invalidate()
' Application.DoEvents()
Next
oCanvas.Save("BrownianTree.bmp")
BackgroundImage = oCanvas
End Sub
' Check adjacent pixels for an illuminated pixel. Private Function CheckAdjacency(ByVal XY As Point) As Boolean
Dim n As Integer = 0
For y As Integer = -1 To 1
' Make sure not to drop off the top or bottom of the image.
If (XY.Y + y < 0) OrElse (XY.Y + y >= iCanvasHeight) Then Continue For
For x As Integer = -1 To 1
' Make sure not to drop off the left or right of the image.
If (XY.X + x < 0) OrElse (XY.X + x >= iCanvasWidth) Then Continue For
' Don't run the test on the calling pixel.
If y <> 0 AndAlso x <> 0 Then
n = (XY.Y + y) * iCanvasWidth + (XY.X + x)
If iPixels(n) = iSeedColor Then Return True
End If
Next
Next
Return False
End Function
Private Function GetData(ByVal Map As Bitmap) As Integer()
Dim oBMPData As BitmapData = Nothing Dim oData() As Integer = Nothing
oBMPData = Map.LockBits(New Rectangle(0, 0, Map.Width, Map.Height), ImageLockMode.ReadOnly, PixelFormat.Format32bppArgb)
Array.Resize(oData, Map.Width * Map.Height)
Runtime.InteropServices.Marshal.Copy(oBMPData.Scan0, oData, 0, oData.Length)
Map.UnlockBits(oBMPData)
Return oData
End Function
Private Sub SetData(ByVal Map As Bitmap, ByVal Data As Integer())
Dim oBMPData As BitmapData = Nothing
oBMPData = Map.LockBits(New Rectangle(0, 0, Map.Width, Map.Height), ImageLockMode.WriteOnly, PixelFormat.Format32bppArgb)
Runtime.InteropServices.Marshal.Copy(Data, 0, oBMPData.Scan0, Data.Length)
Map.UnlockBits(oBMPData)
End Sub
Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load DoubleBuffered = True BackgroundImageLayout = ImageLayout.Center Show() Activate() Application.DoEvents() BrownianTree() End Sub
End Class </lang>
Final output:
- WikipediaSourced
- Raster graphics operations
- Programming Tasks
- Fractals
- AutoHotkey
- BBC BASIC
- C
- FreeImage
- C sharp
- System.Drawing
- D
- Delphi
- Fantom
- Fortran
- Go
- Haskell
- Icon
- Unicon
- Icon Programming Library
- J
- Java
- Swing
- AWT
- JavaScript
- Liberty BASIC
- Lua
- Mathematica
- OCaml
- Octave
- Perl
- PicoLisp
- PureBasic
- Python
- Pygame
- REXX
- Ruby
- RMagick
- Run BASIC
- Scheme
- Seed7
- Tcl
- Tk
- Visual Basic .NET