<?php

$width = 800;
$height = 600;
$scale = $height;
$zoomfact = 1.5;
$x0 = -.5;
$y0 = 0;

$nmax = 80;

$gd = imagecreatetruecolor($width, $height);

for ($nx = 0; $nx < $width; $nx++)
{
    for($ny = 0; $ny < $height; $ny++)
    {
        $xt = (4 / $scale) * ($nx - $width/2) / $zoomfact + $x0;
        $yt = (4 / $scale) * ($ny - $height/2) / $zoomfact + $y0;

        $x = $xt;
        $y = $yt;

        for($i = 0; $i < $nmax; $i++)
        {
            $xn = pow($x, 2) - pow($y, 2) + $xt;
            $yn = 2 * $x * $y + $yt;

            if(pow($xn, 2) + pow($yn, 2) > 4)
            {
                $color = imagecolorallocate($gd, $i<<4%255, $i<<4%255, $i<<4%255);
                imagesetpixel($gd, round($nx),round($height - $ny), $color);
                break;
            }

            $x = $xn;
            $y = $yn;
        }
    }
}

header('Content-Type: image/png');
imagepng($gd);

?>