Quaternion?

[Kali]

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:





As you can see I only used 3-dimensional vectors, so... what's the mathematical explanation for this?   

Could it be that when z.w=0, the multiplication is done like I did?

[Syntopia]

As you can see I only used 3-dimensional vectors, so... what's the mathematical explanation for this?   
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 :-)

[Kali]

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