3D mandelbulb generated by VEX code in houdini

Mandelbulb

//---Functions---


/*
r = sqrt(x*x + y*y + z*z )
theta = atan2(sqrt(x*x + y*y) , z)
phi = atan2(y,x)

newx = r^n * sin(theta*n) * cos(phi*n)
newy = r^n * sin(theta*n) * sin(phi*n)
newz = r^n * cos(theta*n)
*/

function int Mandel(float x0, y0, z0; int imax){
    float x, y, z, xnew, ynew, znew, n=ch("n"), r, theta, phi;
    int i;
    
    x = x0;
    y = y0;
    z = z0;
    
    for(i=0; i < imax; i++){
        //xnew = x*x - y*y + x0;
        //ynew = 2 * x * y + y0;
        
        r = sqrt(x*x + y*y + z*z );
        theta = atan2(sqrt(x*x + y*y) , z);
        phi = atan2(y,x);
        
        xnew = pow(r, n) * sin(theta*n) * cos(phi*n) + x0;
        ynew = pow(r, n) * sin(theta*n) * sin(phi*n) + y0;
        znew = pow(r, n) * cos(theta*n) + z0;
        if(xnew*xnew + ynew*ynew > 8){
            return(i);
        }
        
        x = xnew;
        y = ynew;
        z = znew;
    }
    return(imax);
}


//--- Main ---

int maxiter = 60;

if(Mandel(@P.x, @P.y, @P.z, maxiter) < maxiter){
    @density = 0.0;
}
else{
    @density = 1.0;
}