Diffusion-Limited Aggregation creates great looking fractals, I made a fast(but not the fastest) Diffusion-Limited Aggregation simulator. You define how many molecules will be released and the size of the board. A more accurate Brownian motion system will make the image look better, but it is going to be a lot slower.
Don't assign numbers larger than 700 for step, it is going to consume a huge amount of time to generate. A size 100 step 700 image cost around 60 seconds.
A faster version can be implemented by change the random movement of molecules into linear movement.
set_time_limit(0);
//Very fast Diffusion-Limited Aggregation
$s = 100;
$step = 700;
$area = 2;//smaller = faster, larger = more accurate(random)
$image = imagecreate($s,$s);
imagecolorallocate($image,255,255,255);
$color = imagecolorallocate($image,0,0,0);
$s2 = $s/2;
$grid[$s2][$s2] = 1;
imagesetpixel($image,$s2,$s2,$color);
while($i<$step){
//calculate releasing area
$n = max($max_x - $min_x, $max_y - $min_y) + $area;
$s2mn = $s2-$n;
$s2an = $s2+$n;
//release a molecule
do{
$x = rand($s2mn,$s2an);
$y = rand($s2mn,$s2an);
}while($grid[$x][$y]);
//move the molecule randomly
while(!($grid[$x-1][$y-1]+$grid[$x-1][$y]+$grid[$x-1][$y+1]+
$grid[$x][$y-1]+$grid[$x][$y+1]+$grid[$x+1][$y-1]+
$grid[$x+1][$y]+$grid[$x+1][$y+1])){
$x += rand(-1,1);
$y += rand(-1,1);
if($x<$s2mn||$x>$s2an||$y<$s2mn||$y>$s2an){
continue 2;
}
}
$grid[$x][$y] = 1;
if($max_x<$x){
$max_x = $x;
}elseif($min_x>$x){
$min_x = $x;
}
if($max_y<$y){
$max_y = $y;
}elseif($min_y>$y){
$min_y = $y;
}
imagesetpixel($image,$x,$y,$color);
++$i;
}
header("Content-type: image/png");
imagepng($image);
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