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float DE(vec3 z0){//MandelBulb by twinbee (sine version)
	vec4 c = vec4(z0,1.0),z = c;
	float r = length(z),zr,zo,zi,p=8.0;//p is the power
	for (int n = 0; n < 7 && r<2.0; n++) {
		zo = asin(z.z / r) * p;//add phase shifts here
		zi = atan(z.y, z.x) * p;//...and here
		zr = pow(r, p-1.0);
		z=zr*vec4(r*vec3(cos(zo)*vec2(cos(zi),sin(zi)),sin(zo)),z.w*p)+c;
		r = length(z.xyz);
	}
	return 0.5 * log(r) * r / z.w;
}

            // some debugging to show the difference
            vec3 ray2 = eye + tmin * ray_direction;
            pixel_color.r = DE_blog (ray2, tmin) / bailout;
            pixel_color.g = DE_forum(ray2, tmin) / bailout;
            pixel_color.b = DE      (ray2, tmin) / bailout;

Error: Globals.shaders[file.substr(...)] is undefined DisplaySource@http://www.kinostudios.com/mandelbulb.html:97 updateMenu@http://www.kinostudios.com/mandelbulb.html:119 @http://www.kinostudios.com/mandelbulb.html:129 Scope.prototype.$eval@http://cdnjs.cloudflare.com/ajax/libs/angular.js/1.1.5/angular.js:8926 Scope.prototype.$apply@http://cdnjs.cloudflare.com/ajax/libs/angular.js/1.1.5/angular.js:9006 @http://www.kinostudios.com/mandelbulb.html:128 x.event.dispatch@http://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js:5 x.event.add/y.handle@http://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js:5

void main()
{
   gl_Position = ftransform();//same as:  gl_Position = gl_ModelViewProjectionMatrix * gl_vertex;
}

varying vec3 rayDir;

void main( void )
{
   gl_Position = gl_Vertex;//shouldn't be transformed
   
   vec4 WPpos = gl_ModelViewProjectionMatrixInverse*gl_Vertex;//
   WPpos /= WPpos.w;
   rayDir=WPpos.xyz-gl_ModelViewMatrixInverse[3].xyz;
}

varying vec3 rayDir;
vec3 eyePos=gl_ModelViewMatrixInverse[3].xyz;//or just send it as uniform
...
...
void main()
{
   vec3 rayDir = normalize(rayDir);
   gl_FragColor=rayTrace(eyePos, rayDir);
}

var vertexPositions = [
  1.0, 1.0, 0.0,
  -1.0, 1.0, 0.0,
  1.0, -1.0, 0.0,
  -1.0, -1.0, 0.0
];

        var modelViewProjectMatrixInverse = new THREE.Matrix4();

        function render() {
            uniforms.time.value += 0.05;
            controls.update( clock.getDelta() );

            modelViewProjectMatrixInverse.multiplyMatrices(camera.matrixWorldInverse, mesh.matrixWorld).multiply(camera.projectionMatrix)
            modelViewProjectMatrixInverse.getInverse(modelViewProjectMatrixInverse);
            uniforms.modelViewProjectMatrixInverse.value = modelViewProjectMatrixInverse;
            
            renderer.render( scene, camera );
        }

// #define USE_KNIGHTY

modelViewProjectMatrixInverse.multiplyMatrices(camera.projectionMatrix, camera.matrixWorldInverse).multiply(mesh.matrixWorld);

    vec4 WPpos = modelViewProjectMatrixInverse * gl_Position;
    WPpos /= WPpos.w;
    rayDir = WPpos.xyz - modelMatrix[3].xyz;

    rayDir = (modelViewMatrix * gl_Position).xyz;

bool intersectBoundingSphere(vec3 origin,
    vec3 direction,
    out float tmin,
    out float tmax)
{
    bool hit = false;

    float b = dot(origin, direction);
    float c = dot(origin, origin) - bounding*bounding;
    float disc = b*b - c;         // discriminant
    tmin = tmax = 0.0;

    if (disc > 0.0) {
        // Real root of disc, so intersection
        float sdisc = sqrt(disc);
        
        tmin=max(0.,-b - sdisc);//DE(origin + max(0.,t0) * direction, min_dist);//
        tmax=max(0.,-b + sdisc);//max(0.,t0)+t1;
        hit = true;
    }

    return hit;
}

        function render() {
            controls.update( clock.getDelta() );

            // BUG!! in three.js (at least r59). we need to calculate the 
            // matrixWorldInverse here ourselves, otherwise we'll get a
            // jittery effect.
            camera.updateMatrixWorld();
            camera.matrixWorldInverse.getInverse( camera.matrixWorld );

            uniforms.time.value += 0.05;
            modelViewProjectMatrixInverse.multiplyMatrices(camera.projectionMatrix, camera.matrixWorldInverse).multiply(mesh.matrixWorld);
            modelViewProjectMatrixInverse.getInverse(modelViewProjectMatrixInverse);
            uniforms.modelViewProjectMatrixInverse.value = modelViewProjectMatrixInverse;
            
            renderer.render( scene, camera );
        }

            pixel_color.g /= cos(pow(sin(phase.x),phase.y));
            pixel_color.r *= -ray_length -dist * tan(pow(phase.x, pixel_color.g));
            pixel_color.b /= DE(ray, dist)* sin(phase.y) ;
            pixel_color.a = 1.0;

            pixel_color.g /= cos(pow(sin(phase.x),phase.y));
            pixel_color.r /= tan(pow(float(i), cos(float(i))));
            pixel_color.b /= sin(pow(phase.y, sin(phase.y)));
            pixel_color.a = 1.0;

// FROM: http://www.fractalforums.com/index.php?topic=16793.msg64299#msg64299
float DE(vec3 z0, inout float min_dist){//MandelBulb by twinbee
    vec4 z = vec4(z0,1.0), c = z;
    float r = length(z.xyz),zr,theta,phi,p=power;//p is the power
    phi = atan(z.y, z.x) * p;// th = atan(z.y, z.x) + phase.x; ...and here
    theta = asin(z.z / r) * p;// ph = acos(z.z / r) + phase.y; add phase shifts here 
    min_dist = min(min_dist, r);
    for (int n = 0; n < MAX_ITERATIONS; n++) {
        zr = pow(r, p-1.0);
        z=zr*vec4(r*vec3(sin(theta)*vec2(cos(phi),sin(phi)),cos(theta)),z.w*p)+c; // this version was from the forums
        r = length(z.xyz);
        min_dist = min(min_dist, r);
        if (r > bailout) break;
        phi = (atan(z.y, z.x) + phase.x) * p;// th = atan(z.y, z.x) + phase.x; ...and here
        theta = (acos(z.z / r) + phase.y) * p;// ph = acos(z.z / r) + phase.y; add phase shifts here  
    }
    return 0.5 * log(r) * r / z.w;
}