Originally conceived by Ben Mansell in his favourite pub in Cambridge, the TrafficScript Mandelbrot generator has been wowing network managers for years! Who would have thought a piece of networking gear could generate a picture as great as this? If you've not seen this demo of TrafficScript before, now is a great time to try it out.
The eponymous Mandelbrot Set is the subset of complex numbers that don't diverge to infinity when a particular mathematic operation is repeatedly applied. It has a distinctive fractal (infinitely complex) boundary, and you can create some beautiful renderings of the set by coloring the points in the complex plane by how quickly they do diverge:
The following TrafficScript rule endeavors against all the odds to render such a picture in your browser, with full support for zooming in on the intricate boundary. Attach it as a request rule to an HTTP virtual server and start exploring...
# Mandelbrot set generator in TrafficScript.
$pixelSize = 4;
$rows = 60;
$cols = 60;
$magfactor = 4;
$maxiter = 255;
$path = http.getPath();
if( $path == "/" ) {
# Get the area of the mandelbrot set to view
$minx = lang.toDouble( http.getFormParam( "minx" ));
$miny = lang.toDouble( http.getFormParam( "miny" ));
$maxx = lang.toDouble( http.getFormParam( "maxx" ));
$maxy = lang.toDouble( http.getFormParam( "maxy" ));
if( !$minx ) $minx = -2.0;
if( !$miny ) $miny = -1.25;
if( !$maxx ) $maxx = 0.5;
if( !$maxy ) $maxy = 1.25;
$width = $maxx - $minx;
$height = $maxy - $miny;
$stepx = $width / $cols;
$stepy = $height / $rows;
$w2 = $width / $magfactor;
$h2 = $height / $magfactor;
$grid = "";
$img = '<img width="'.$pixelSize.'" height="'.$pixelSize.'" src="s.gif?x=';
for( $yval = $maxy; $yval > $miny; $yval -= $stepy ) {
# Build the grid line-by-line... it's more efficient
$line = "";
$aref = '<a href="https://community.pulsesecure.net/?miny=' . ($yval-$h2) . '&maxy=' . ($yval+$h2) . '&minx=';
for( $xval = $minx; $xval < $maxx; $xval += $stepx ) {
$line .= $aref . ($xval-$w2) . '&maxx=' . ($xval+$w2) . '">'
. $img . $xval . '&y=' . $yval . '"/></a>';
}
$grid .= $line . "<br>\n";
}
# Deliver the web page
$page = '
<html><head><title>Mandlebrot</title>
<style type="text/css">img { border: none; }</style>
</head><body>' . $grid . '
<a href=/>Zoom back out</a></body></html>';
http.sendResponse( "200 OK", "text/html", $page, "" );
}
if( $path == "/s.gif" ) {
# Calculate the colour of point x,y of the mandelbrot and return an image
# real and imaginary components of c, based on the co-ordinates
$cr = lang.toDouble( http.getFormParam( "x" ));
$ci = lang.toDouble( http.getFormParam( "y" ));
# The main loop. It calculates z=z*z+c, and loops until z*z >= 2
$zr = 0.0;
$zc = 0.0;
$n = 0;
for( ; $n <= $maxiter; $n++ ) {
$zrs = $zr * $zr;
$zis = $zi * $zi;
if(( $zrs + $zis ) >= 4.0 ) break;
$zi = 2 * $zr * $zi + $ci;
$zr = $zrs - $zis + $cr;
}
# Use $n to generate the color; $n >= $maxiter means (x,y) is in set
# An 8x8 GIF, completely black
$image = string.hexDecode( "47494638376108000800800100000000ffffff2c".
"0000000008000800000207848fa9cbed5d00003b" );
if( $n < $maxiter ) {
$i = lang.toDouble($n)/lang.toDouble($maxiter);
$i = math.sqrt( math.sqrt( $i ) );
# Orange #e16832
$r = 0xe1*math.sqrt( $i );
$g = 0x68*$i;
$b = 0x32*$i;
# Replace bytes 13, 14 and 15
$image = string.replaceBytes( $image, lang.chr( $r ), 13 );
$image = string.replaceBytes( $image, lang.chr( $g ), 14 );
$image = string.replaceBytes( $image, lang.chr( $b ), 15 );
}
http.sendResponse( "200 OK", "image/gif", $image, "" );
}
The rule works in two steps.
- When called with the URL '/', it generates a grid of images (s.gif), each image having a querystring identifying its location in the grid
- When invoked with a request for the image, the rule performs the Mandelbrot iteration for the image location and returns a gif that is colored according to the result of the iteration
Be warned that trying to render a grid greater than 60x60 (i.e. 3600 concurrent image requests) can stretch the capabilities of your browser and networking stack, and certainly gave my development VM a good workout! For note, Safari coped a lot better at loading and rendering the page than Google Chrome did.
Note: There's a built-in guard in Traffic Manager to abort run-away TrafficScript rules. If you find that you're not getting any output, and you have a 'maxinstr' error in your event log, try increasing the value of trafficscript!max_instr to a larger value.
This article originally contributed by owen
