Fractals in PHP

Introduction

A little PHP script to generate fractals using the Mandlebrot set.

Why? Because you can...

Output

This 500x500 image took about two minutes to generate on a 3GHz Pentium 4.

Code

<?php
/* Timing */
set_time_limit(0);
function microtime_float() {
    list($usec, $sec) = explode(" ", microtime());
    return ((float)$usec + (float)$sec);
}

$time_start = microtime_float();

/* Lil Mandlebrot Set Fractal Generator */
define ('IMAGE_WIDTH', 100);
define ('IMAGE_HEIGHT', 100);

define ('X_MIN', -1.5);
define ('X_MAX', 0.5);
define ('Y_MIN', -1);
define ('Y_MAX', 1);

define ('MAX_ITERATIONS', 200); // if you change this to a number bigger than 200, make sure you create a new palette.png

header("Content-type: image/png");
$image = imagecreate(IMAGE_WIDTH, IMAGE_HEIGHT);

// Load the palette to find colours
$colours = array();
$colours['inside'] = imagecolorallocate($image, 0, 0, 0);

$palette = imagecreatefrompng("palette.png");
for ($i=0; $i<imagesx($palette); $i++) {
    $rgb = imagecolorat($palette, $i, 0);
    $colours[$i] = imagecolorallocate($image, ($rgb >> 16) & 0xFF, ($rgb >> 8) & 0xFF, $rgb & 0xFF);
}

for ($i=0; $i<IMAGE_WIDTH; $i++) {
    for ($j=0; $j<IMAGE_HEIGHT; $j++) {
        // What values of x and y does this pixel represent?
        $x = X_MIN+$i*((X_MAX - X_MIN) / (IMAGE_WIDTH-1));
        $y = Y_MIN+$j*((Y_MAX - Y_MIN) / (IMAGE_HEIGHT-1));
        
        // C=x+yi
        
        $iteration = 0;
        $z = array(0,0); // The initial value of z is 0+0i
        $magnitude = 0;
        
        // Optimization: Store x^2 and y^2 so we don't have to keep calculating it
        $x2 = 0;
        $y2 = 0;
        
        // If the |z| > 2 ever, then the sequence will tend to infinity so we can exit the loop
        while ($iteration <= MAX_ITERATIONS && $x2+y2 <= 4) {
            // In order to get the next term in the sequence
            // we need to square the previous number and then add
            // the original complex number
            //
            // z(n+1) = z(n)^2+c
            
            $k = $z;
            
            // z is a complex number. When we square a complex number in the form x+yi:
            // New real component: x^2-y^2
            // New imaginary component: 2*real*imaginary
            $z[0] = $x2 - $y2;
            $z[1] = 2 * $k[0] * $k[1];
            
            // Add Complex Number
            $z[0] = $z[0] + $x;
            $z[1] = $z[1] + $y;
            
            $x2 = pow($z[0], 2);
            $y2 = pow($z[1], 2);
            
            ++$iteration;
        }
        
        if ($iteration == MAX_ITERATIONS) {
            imagesetpixel($image, $i, $j, $colors['inside']);
        } else {
            imagesetpixel($image, $i, $j, $colours[$iteration]);
        }
        
    }
}

$time_end = microtime_float();
header ("X-Exec-Time: ".($time_end - $time_start));

imagepng($image);
?>

To run this script, you'll need a copy of the image palette. Save the file as palette.png and place it in the same folder as the fractal generator.

Written By:

cow.neondragon.net