Title: Quaternion? Post by: Kali on March 19, 2012, 06:22:46 AM I don't know too much about quat fractals, but I definitely got one (or something like them), by choosing a julia using this formula:
x0 = z.x; z.x = z.x * z.x - z.y * z.y - z.z * z.z; z.y = 2.00 * x0 * z.y; z.z = 2.00 * x0 * z.z; z = z + c; I modified Fragmentarium's Mandelbulb.frag and this is the result: (http://img254.imageshack.us/img254/7767/rarequaternion.jpg) As you can see I only used 3-dimensional vectors, so... what's the mathematical explanation for this? :hmh: Could it be that when z.w=0, the multiplication is done like I did? Title: Re: Quaternion? Post by: Syntopia on March 19, 2012, 07:06:37 PM As you can see I only used 3-dimensional vectors, so... what's the mathematical explanation for this? :hmh: Could it be that when z.w=0, the multiplication is done like I did? Exactly, the square of a quaternion is: (x*x-y*y-z*z-w*w, 2*x*y, 2*xz, 2*xw) So you discovered a slice of quaternion algebra by chance :-) Title: Re: Quaternion? Post by: Kali on March 19, 2012, 07:14:01 PM Exactly, the square of a quaternion is: (x*x-y*y-z*z-w*w, 2*x*y, 2*xz, 2*xw) So you discovered a slice of quaternion algebra by chance :-) Nice! Too bad this was already discovered some time ago ;D |