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// Created by inigo quilez - iq/2013
// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
// This shader computes the distance to the Mandelbrot Set for everypixel, and colorizes
// it accoringly.
//
// Z -> Z²+c, Z0 = 0.
// therefore Z' -> 2·Z·Z' + 1
//
// The Hubbard-Douady potential G(c) is G(c) = log Z/2^n
// G'(c) = Z'/Z/2^n
//
// So the distance is |G(c)|/|G'(c)| = |Z|·log|Z|/|Z'|
//
// More info here: http://www.iquilezles.org/www/articles/distancefractals/distancefractals.htm
void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
vec2 p = -1.0 + 2.0 * fragCoord.xy / iResolution.xy;
p.x *= iResolution.x/iResolution.y;
// animation
float tz = 0.5 - 0.5*cos(0.225*iTime);
float zoo = pow( 0.5, 13.0*tz );
vec2 c = vec2(-0.05,.6805) + p*zoo;
// iterate
float di = 1.0;
vec2 z = vec2(0.0);
float m2 = 0.0;
vec2 dz = vec2(0.0);
for( int i=0; i<300; i++ )
{
if( m2>1024.0 ) { di=0.0; break; }
// Z' -> 2·Z·Z' + 1
dz = 2.0*vec2(z.x*dz.x-z.y*dz.y, z.x*dz.y + z.y*dz.x) + vec2(1.0,0.0);
// Z -> Z² + c
z = vec2( z.x*z.x - z.y*z.y, 2.0*z.x*z.y ) + c;
m2 = dot(z,z);
}
// distance
// d(c) = |Z|·log|Z|/|Z'|
float d = 0.5*sqrt(dot(z,z)/dot(dz,dz))*log(dot(z,z));
if( di>0.5 ) d=0.0;
// do some soft coloring based on distance
d = clamp( pow(4.0*d/zoo,0.2), 0.0, 1.0 );
vec3 col = vec3( d );
fragColor = vec4( col, 1.0 );
}
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