Hi
I have just render my first 3D Mandelbrot with z in 3-rd power:
z(n+1) = z(n)^3 + p
where z is Quatermion:
z = ra + ib + jc + kd
multiplying rules:
r*i = i; r*j = j; r*k=k;
r*r=r; i*i=-1; j*j=-1; k*k=-1;
i*j = k; j*k=i; k*i=j;
I used 4D Quaternions to make 4D formula for render 3D fractal on 2D screen :-). After very long multiplying on paper (two A4 pages :-) I have got following formula for iterations:
newx = x*x*x - 3*(x*y*y + 3*x*z*z + 3*x*w*w) - 6*y*z*w + a
newy = -y*y*y + 3*(x*x*y - y*z*z - y*w*w) + 6*z*z*w + b
newz = -z*z*z + 3*(x*x*z - z*y*y - z*w*w) + 6*x*y*w + c
neww = -w*w*w + 3*(x*x*w - w*y*y - w*z*z) + 6*x*y*z + d (d = 0)
full resolution:
http://picasaweb.google.com/buddhi1980/Fraktale#5360064631222029058Nice to see that it seems to "work" at higher powers too
Just a small point - you shouldn't really call it quaternionic because quaternions are a very specific 4D number form not a general term for 4D number systems and this system is quite different from the quaternions
May 19, 2010, 09:51:09 AM
Dilber MC Theme by HarzeM