shadertoy.txt

//FRAGMENT SHADER
#ifdef GL_ES
precision mediump float;
#endif
#define RE_START -2.
//or float x = 2.0;
//or float x - float(2);
#define RE_END    1.
#define IM_START -1.
#define IM_END    1.
#define MAX_ITER 359 

//fragCoord is current pixel
//main loops the entire program every pixel

//vec2 simpleComplex(vec2 xy) {
//    vec2 result;
//    result.x = (RE_START + (xy.x/iResolution.x) * float(RE_END - RE_START));
//	result.y = (IM_START + (xy.y/iResolution.y) * float(IM_END - IM_START));
//	return result;        
//}

int mbrot(vec2 c) { 
    vec2 zed;
    zed.x = 0.0;
    zed.y = 0.0;    
    int n = 0;
    //https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-complex-number
    while (sqrt(pow(zed.x,2.0) + pow(zed.y,2.0)) <= 2.0 && n < MAX_ITER) { 
        //zed = zed*zed + c;
        zed = vec2 (pow(zed.x,2.0)-pow(zed.y,2.0),2.0 *zed.x * zed.y);
    	zed.x = (zed.x + c.x);
    	zed.y = (zed.y + c.y);    
		//http://mathworld.wolfram.com/ComplexAddition.html        
		n+=1;
    }
    return n;
}
//function from @Nemes#8370
vec4 hue2rgb(float hue) {
    vec4 K = vec4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
    vec3 p = abs(fract(hue + K.xyz) * 6.0 - K.www);
    return vec4(clamp(p - K.xxx, 0.0, 1.0), 1.0);
}


void mainImage( out vec4 fragColor, in vec2 fragCoord ) {
    fragColor = vec4(0.,0.,0.,1.)
    vec2 uv = fragCoord.xy/iResolution.xy;
	float aspect = iResolution.y/iResolution.x;
	vec2 p = uv*2.-1.; // transform uv range(0-1) to be centered and normalized(-1-1)
    p.y*=aspect;
    int n = mbrot(p*2.); // *2. is the zoom value to create a variable for controlled by GUI
    float B = float(n)*8./float(MAX_ITER); 
	//float B = float(n)/float(MAX_ITER);
	vec4 color = hue2rgb(B);
    fragColor = color;
}