Hi. Here's a piece of equation art that evolved after playing around with a piece of code Rhapsody and I wrote together.

Programming:


Thanks for all the equation art inspiration:


Technical details:
This was rendered using PHP and the GD graphics library. The shape evolves from an intersection of circles and pedals drawn around a center point with various radio values each in constant distance from the next.

The flames are created by using a flood fill algorithm and restricting it in resolution to create areas that get filled. Anti aliasing is disabled in purpose to achieve these beautiful fillings by taking advantage of areas the get closer as we approach the center of the shape.

Pedals are drawn using the absolute value of the sinus function and using a circle at the same center as the rest as an x axis and the circle's perpendicular vector at each point as the y axis.

If you're a programmer, you can use PHP to render it yourself. Here's the code. Feel free to use it and modify it for any need. Feel free to leave a comment for any questions you may have, including mathematics or programming questions relevant to this piece. Constructive critique is also very welcome

<?php
/*
Copyright 2009 (c)
<rhapsody@kamibu.com>
<dionyziz@kamibu.com>
Licensed under the MIT license: [link]
*/

function line( $img, $x1, $y1, $x2, $y2, $color ) {
$tranz1 = transform( $x1, $y1 );
$tranz2 = transform( $x2, $y2 );

imageline( $img, $tranz1[ 'x' ], $tranz1[ 'y' ], $tranz2[ 'x' ], $tranz2[ 'y' ], $color );
}
function transform( $x, $y ) {
$transx = CENTERX + $x;
$transy = CENTERY - $y;

return array( 'x' => $transx, 'y' => $transy );
}
function sinabs( $theta ) {
return abs( sin( $theta ) );
}
function drawPedals( $img, $radio, $pedals, $color ) {
for ( $theta = -0.1; $theta <= 2 * pi(); $theta += 0.001 ) {
$transradio = $radio + sinabs( $theta * $pedals / 2 ) * 100;

$x = $transradio * cos( $theta );
$y = $transradio * sin( $theta );

if ( isset( $prevx ) ) {
line( $img, $x, $y, $prevx, $prevy, $color );
}
$prevx = $x;
$prevy = $y;
}
}
function flower() {
header( 'Content-type: image/png' );

define( 'WIDTH', 1024 );
define( 'HEIGHT', 1024 );
define( 'CENTERX', WIDTH / 2 );
define( 'CENTERY', HEIGHT / 2 );

$img = imagecreatetruecolor( WIDTH, HEIGHT );

$white = imagecolorallocate( $img, 255, 255, 255 );
$black = imagecolorallocate( $img, 0, 0, 0 );
$red = imagecolorallocate( $img, 255, 0, 0 );
$yellow = imagecolorallocate( $img, 255, 255, 0 );

imagefill( $img, 0, 0, $white );

$fadevar = 0;
$centerradio = 500;

for ( $r = $centerradio; $r; $r -= 5 ) {
drawPedals( $img, 300 - $r, 10, $black );
imagefill( $img, CENTERX + $centerradio + 1 , CENTERY + $centerradio + 1, $red );
}
for ( $r = $centerradio; $r; $r -= 5 ) {
$fadevar += 2;
$centercolor = imagecolorallocate( $img, 255, 255, $fadevar );
imagearc( $img, CENTERX, CENTERY, 2 * $r, 2 * $r, 0, 360, $centercolor );
imagefill( $img, CENTERX, CENTERY, $centercolor );
}

imageconvolution( $img, array( array( 1, 2, 1 ), array( 2, 4, 2 ), array( 1, 2, 1 ) ), 16, 0 );
imagepng( $img );
}
flower();
?>